Arrange a rack in center of oven; preheat to 350°. In a large bowl, using a handheld mixer on medium-high speed (or in the large bowl of a stand mixer fitted with the paddle attachment), beat butter, brown sugar, salt, and 1¼ c. (250 g.) granulated sugar until light and creamy, 1 to 2 minutes. Add egg, egg yolk, and vanilla and beat, scraping down bowl with a spatula, until just combined. Add baking powder and baking soda and beat until incorporated.

Reduce mixer speed to low and add half of flour. Beat until only a few streaks remain, then add remaining flour and beat until incorporated.

Place remaining ½ c. granulated sugar in a small shallow bowl. Using a 1-oz. cookie scoop or 2 spoons, scoop dough into balls about 2 Tbsp. (1 oz.) each. Roll half of the balls in granulated sugar (reserve sugar for remaining dough) and arrange on 2 parchment-lined baking sheets, spacing at least 2" apart. Refrigerate remaining unsugared dough balls until ready to bake. (You can also refrigerate all dough balls before coating in sugar in an airtight container at least 1 hour and up to 2. This gives them a richer flavor.)

Bake sugar cookies, rotating sheets top to bottom after 7 minutes, until just tinged with golden brown around the edges, 10 to 14 minutes.

Let cookies cool 5 minutes on sheets, then transfer to a wire rack and let cool completely. Repeat with remaining dough and reserved granulated sugar.

Make Ahead: Cookies can be made 3 days ahead. Store in an airtight container at room temperature.