First, we make sure that every interviewer, including initial contacts and phone screens, offers the candidate a chance to ask their own questions and I make it a point to state that "you're picking us just as much as we're picking you". From the questions the candidate asks, we get some insight into what's on their mind and they get their questions answered and can form a more informed opinion of us as well.
Second, we generally schedule an informal lunch in our cafeteria (we buy, of course) with the candidate and a 1-3 of our engineers, often from the team they're interviewing with but sometimes just other non-team peers. This is explicitly meant to be informal and similar-level peers, but you can't help sharing data about who we are, how we interact with each other and the candidate, and learning/teaching whether there's likely a good fit.
If you're asking about creating/enhancing cultural fit once hired, that's an ordinary leadership challenge.
A formalized process of informality. Interesting.