Peszek graduated from the Department of Drama at the State Drama School in Kraków. He made his debut in 1966 in Bertold Brecht's The Resistible Rise of Arturo Ui produced at the Polish Theatre in Wrocław. He played there for nine seasons with such outstanding directors as Jerzy Krasowski (The Danton Case by Stanisława Przybyszewska, July 6 by Mikhail Shatrov, and The Revenge by Aleksander Fredro), Krystyna Skuszanka (The Silver Dream of Salomea by Juliusz Słowacki, The Royal Hunt of the Sun by Peter Shaffer, William Shakespeare's The Tempest), Bohdan Korzeniewski (Scapin's Deceits by Molière) and Henryk Tomaszewski (Stanisław Wyspiański's Protesilas and Laodamia).
Peszek moved from Wrocław to the Nowy Theatre in Łódź, where he performed in plays by Kazimierz Dejmek, including Plato's The Apology of Socrates, Antoni Słonimski's Obecność (Presence) and Friedrich Dürrenmatt's The Appointed Time. Nonetheless it was not Dejmek or Krasowski who shaped the young actor but the playwright and composer, Bogusław Schaeffer.
In an interview with the Gazeta Wyborcza daily the actor said:
(…) something happened during my third year of studies that changed my life. I ran into Adam Kaczyński's and Bogusław Schaeffer's company MW2. It was such a shock for me that I, a young man on the verge of adulthood, began to mature really fast. It turned out that you could try to talk about people using an entirely different language, from a perspective unknown to me. Schaeffer's world is smashed into microelements which have to be arranged in order to show pictures of individual situations. I figured it was too fitting to the world I was living in.
Thanks to Schaeffer's influence Peszek started to experiment and to search for new forms of expression in acting. He began creating an individual theatrical language, slightly ludicrous, which avoided an excess of psychology. This style worked perfectly in contemporary plays, especially in those written by Gombrowicz, Mrożek and Różewicz. In his pursuit Peszek received support from Mikołaj Grabowski, actor and director who in his own plays commented on Polish tradition and the present showing them in a distorted mirror. Peszek collaborated with Grabowski in Stefan Jaracz Theatre in Łódź and Stary Theatre in Kraków. Peszek's style took a distanced perspective on the characters he played. His skill for sudden transformation worked wonderfully in Grabowski's productions of Mrożek's The Serenade and The Trainee Fox, Gombrowicz's Trans-Atlantic, as well as Schaeffer's The Quartet and The Script for Three Actors. In 1985, during his collaboration with Grabowski, Peszek created his own manifesto of the language of acting, a monodrama titled Script for Schaeffer's potentially instrumental actor.
The 1990s and the turn of the new century proved the most mature period in Peszek's career. The actor has starred in contemporary works by Krystian Lupa (Dostoyevski's The Brothers Karamazov), Jerzy Jarocki (Jerzy S. Sito's Słuchaj Izraelu [Listen, Israel]), Andrzej Wajda (Yukio Mishima's Mishima), Jerzy Grzegorzewski (Tolstoy's The Death of Ivan Ilyich, Molière's Don Juan). He played Henryk in The Wedding written by Gombrowicz (1998) and Stańczyk in The Wedding written by Wyspiański, both directed by Grzegorzewski at the National Theatre. He has been hired by young directors including Zbigniew Brzoza (Peter Turrini's Finally the End), Mariusz Treliński (Lautréamont – sny [Lautréamont: Dreams] based on Lautréamont, Elżbieta Sikora's Wyrywacz serc [The Usurper of Hearts]), as well as Grzegorz Jarzyna (Thomas Vinterberg's and Mogens Rukov's Festen) and Oskaras Korsunovas (Bruno Schulz's Sanatorium under the Sign of the Hourglass). Peszek makes his own original plays in Poland and abroad; his production based on Sanatorium under the Sign of the Hourglass made in Japan was very well received by the audience.
The following years brought Peszek successful roles in Onegin, a play directed by Mariusz Treliński staged in Wielki Theatre National Opera in Warsaw in 2002, and a year later - in Stanisław Radwan's Opera mleczna (Milk Opera), directed by Mikołaj Grabowski, which was played in the National Old Theatre in Kraków. He directed dramas by Shakespeare, Witkacy, Gombrowicz, Ibsen and Pinter, lately - also plays based on novels. In 2011 Jan Peszek directed Wroniec (The Crowe), based on Jacek Dukaj's bestselling novel, in which the reality of the martial state is shown from the point of view of a seven year old boy. A contemporary fairy tale with historical events in the background left the critics and the audience in awe, and the director explained in an interview for Gazeta Wyborcza:
There is something very enticing in showing the reality of the martial state from the child's point of view. The child is free until it stops believing in fairy tales and grows up. It's worth looking at what's happened with the eyes of a free man. Without prejudice and interpretations filtered through our views, political interest and life experience. I don't intend to analyze what the martial state was in a political sense. Nor do I want to search for the guilty ones, to judge them or justify them. The martial state is more of a background in this play than it is its protagonist.
A few months later electrifying news struck the Polish theatre milieu: Jan Peszek is excercising his karate moves in a Buddhist Shaolin monastery - he's gonna be Bruce Lee! The play Enter the Dragon. Trailer direced by Bartosz Szydłowski was named the event of the year even before it premiered. The great actor was accompanied on stage of the Łaźnia Nowa theatre by his son Błażej, who played Brandon Lee. Earlier the crew went on a journey to China to explore the legend - they visited film studios and trained kung-fu with great masters, writing all about in on a blog.
"We want to present Bruce Lee in a grotesque, humorous way. It is going to be a combination of the spectacular Eastern martial arts with the kitch taken out of B movies" - the creators anticipated. The effects were judged by, among others, Witold Mrozek, who wrote for Dwutygodnik:
Szydłowski plays with this nostalgic and a little trashy dimension of Bruce Lee's legend. Before the master himself will arrive to the casting for the trailer, Franek Kimono from the 1980s will come on stage with his famous song King Bruce Lee Karate Master. It is performed by Mariusz Cichoński, whom the audience in Nowa Huta already know from a great role in Wiktor Rubin's Emmigrants. Other amateur actors from the district of Nowa Huta also appear on stage.
Jan and Błażej Peszek played together also in Pojedynek - zabawa w detektywa (Detective) by Anthony Shaffer, a crime play presented in the Polonia Theatre in Warsaw in 2012.