Brown the butter: In a small saucepan, melt the butter over medium heat. Continue cooking, swirling occasionally, until the butter turns golden brown and smells nutty, about 4-5 minutes. Watch carefully — it can go from browned to burnt quickly. Pour into a bowl (including the browned bits!) and refrigerate until solid but still slightly soft, about 30 minutes.

Make the dough: In a medium bowl, whisk together flour, powdered sugar, minced rosemary, and kosher salt. Add the cooled brown butter and mix until a dough forms. It will be crumbly at first but will come together as you work it.

Shape the cookies: Roll the dough into a log about 2 inches in diameter. Wrap in plastic wrap and refrigerate for at least 30 minutes (or up to 3 days).

Slice and top: Preheat oven to 325°F. Line a baking sheet with parchment paper. Slice the log into 1/4-inch rounds and place on the prepared sheet, spacing 1 inch apart. Sprinkle each cookie with a pinch of flaky sea salt.

Bake: Bake for 12-15 minutes, until the edges are just barely golden. The centers may look slightly underdone — that's okay. They'll firm up as they cool.

Cool completely on the baking sheet before serving. These are delicate!