In a large bowl, beat the softened salted butter, powdered sugar, and granulated sugar with an electric mixer on medium-high speed until light and fluffy, about 2-3 minutes.

Add the egg yolks and vanilla extract. Beat on low speed until just combined.

In a separate bowl, whisk together the flour and baking powder. Add the dry ingredients to the butter mixture in two batches, mixing on low speed until a soft dough forms.

Divide the dough in half. Shape each half into a log approximately 2 inches in diameter. Wrap the logs tightly in plastic wrap and refrigerate for at least 2 hours, or until firm.

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

Unwrap one dough log and slice it into 1/3-inch thick rounds. Arrange the cookies on the prepared baking sheet, about 1 inch apart. Brush the tops with the beaten egg wash and sprinkle generously with flaky sea salt.

Bake for 15-20 minutes, rotating the pan halfway through, until the edges are a deep golden brown. Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.