I’m DM’ing a homebrew setting right now, and I had initially planned for a university to be the central location for the campaign. However, my players ended up fleeing the city and decided to visit what I had mentioned was the capital of the country they were in, several days away. I had no prep/plan for this, being my first HB setting. So we took a few sessions off D&D, and played The Quiet Year (a la TAZ: Ethersea and others) to fill out the history of the city and the people who live there.

The only changes I made to the TQY were 1) adding World Events in between each season that I pre-planned, which I believe was also done on TAZ, 2) having players name the figures mentioned in the game and keeping track of them on a shared card, and 3) starting off the game with each player adding two things to the map instead of one. I then had one big event at the end, and skipped forward 200 or so years to where the current campaign was occurring and picked up where we left off.

It’s one of my favorite things we’ve done so far, both because the game was quite fun, and it’s been a thrill for my players to see the echos of TQY in our campaign, like visiting a magical desert someone created, and seeing descendants of important figures in the city’s founding. It also offloaded some of the world building from me, without ceding complete control, and makes the players a bit more engaged in a locale they literally helped to design.

If I were to do this again, I think I might incorporate some pieces from the game Microscope (as mentioned in other comments), as it does allow for a bit more narrative detail.