Brown the butter: Melt butter in a light-colored saucepan over medium heat. Cook, swirling occasionally, until the butter foams, then turns a deep golden brown with nutty-smelling browned bits at the bottom, 5-8 minutes. Pour immediately into a heatproof bowl to stop cooking. Cool until solid but soft (about 20-25 min at room temp or briefly in fridge).

While butter cools, toast pecans on a baking sheet at 350°F (175°C) for 6-8 minutes until fragrant. Let cool completely, then chop finely.

In a medium bowl, whisk together the flour, baking powder, and salt.

In a stand mixer bowl, combine the cooled browned butter, 3/4 cup powdered sugar, and granulated sugar. Beat on medium speed until light and fluffy, about 2-3 minutes.

Beat in the egg yolk and vanilla extract until fully incorporated.

With mixer on low, gradually add the flour mixture until just combined. Fold in the chopped toasted pecans by hand.

Divide dough in half. Shape each half into an 8-inch long log (about 2-inch diameter). Wrap tightly in plastic wrap and refrigerate for at least 2 hours, or overnight.

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.

Unwrap one log and slice into 1/2-inch thick rounds. Place rounds 1 inch apart on prepared baking sheets.

Bake for 12-14 minutes, until the edges are just barely golden. Centers will be soft. Cool on baking sheet for 5 minutes, then transfer to a wire rack to cool completely.

Once completely cool, dust the cookies generously with additional powdered sugar before serving.