Q: What do all these dishes have in common?
A: Brown butter. Which makes them extra delicious.
Brown butter is just regular butter that has been heated until it browns.
Solid butter is actually an emulsion of water and fat, with milk protein solids suspended inside. As it melts, the water evaporates and the milk solids are exposed to heat and start to turn brown.
Sometimes called beurre noisette (which translates literally to hazelnut butter and is so named because it smells like hazelnuts and has a similar nutty color), brown butter has all the great qualities of regular butter, plus a nutty, toasted flavor that makes baked goods and sauces taste that much richer. And, it is a pretty brown color. Basically, it is excellent.