Talk with the DM about when these moments come up, and ask if he's ever against players describing moments in between adventures. As in, describing to each other about how you talk about your past, or your habits. Maybe someone asks the Rogue why he likes to cook all the time.
Sometimes, we feel like we don't have time for small talk in the session, because we all want to be heroes and we don't want to slow it down in any way, so try and flesh those things out when you can't adventure.