Examples of this form (distinct from the interview, though at times these works lapse into it):
Boswell, Life of Johnson
Eckermann, Conversations with Goethe
Richter, Conversations with Bruno Monsaigneon
Traubel, With Walt Whitman in Camden
Some scholarship and secondary reading on conversation:
Gibian, Oliver Wendell Holmes and the Culture of Conversation
Miller, Conversation: A History of a Declining Art
Turkle, Reclaiming Conversation