A childhood friend of mine's mother was from New Mexico, and around Christmas she would make this dish that was increasingly smaller tortillas stacked until it looked kind of like a Christmas tree. There was stuff between the layers, but there very top layer was, like, a solid inch of salt. They'd have it every night for a week or so, and as it sat and was reheated, the salt would slowly dissolve down to the bottom layers. As the salt diffused, the dish would get better each day.
Although he was my best friend for three years (I met him in HS), and practically lived at his house, I was never there for Christmas because we were always traveling to see my extended family, so I never got to experience this. He was absolutely fanatical about it. I always wondered, why not just salt the layers appropriately to begin with? But apparently the process was part of the magic and made the end effect better?
Anyway, when I think of dishes that get better with age, that's the first thing I think about. Even decades later.