Melt the unsalted butter in a saucepan over medium-low heat until foamy and browned, about 5 minutes. Chill until solidified.

Preheat the oven to 350°F (175°C) and sift together the all-purpose flour, baking powder, kosher salt, and baking soda.

Beat the chilled brown butter with dark brown and granulated sugars until light and fluffy, then add the egg and vanilla just until combined.

Gradually mix in the dry ingredients until just combined, then fold in the chopped white chocolate, pistachios, and dark chocolate.

Scoop out 1 tablespoon of dough, roll into balls, and place into a non-stick mini muffin tray.

Bake for about 12-14 minutes; gentle press the centers down with a spoon right after removing from the oven.

Cool the cookie cups in the tray for 15 minutes, then transfer to a wire rack for another 20-30 minutes.

Melt the dark chocolate and drizzle over each filled cookie cup, sprinkling extra pistachios on top.

Refrigerate the cookie cups uncovered until the chocolate sets, store in an airtight container at room temperature for up to one week.