Brown the butter: Add butter to a light-colored saucepan over medium heat. Cook, stirring, until it foams, then turns golden with brown bits at the bottom and smells nutty, 5–7 minutes. Pour into a heatproof bowl, scraping in the browned bits, and cool to room temperature until thickened but not solid.

Whisk dry ingredients: In a separate bowl, whisk flour, baking soda, baking powder, and salt. Set aside.

Cream sugars and butter: In a large mixing bowl, whisk or beat the cooled brown butter with brown sugar and granulated sugar until combined and glossy, about 1–2 minutes.

Add eggs and vanilla: Beat in the egg and egg yolk until the mixture is smooth and slightly thick. Stir in vanilla.

Mix in sourdough starter: Add the starter and mix until fully incorporated. The batter may look slightly silky—this is good.

Add dry ingredients: Fold the flour mixture into the wet ingredients just until a few streaks remain.

Stir in chocolate: Fold in the chocolate, reserving a small handful for topping. Do not overmix.

Chill the dough: Cover and chill for at least 45–60 minutes, or up to 24 hours. This helps the cookies hold their shape and develop flavor.

Preheat and prep: Heat the oven to 350°F (175°C). Line two baking sheets with parchment.

Scoop: Scoop 2-tablespoon mounds (about 45–50 g each) and place 2–3 inches apart. Press a few extra chocolate pieces on top, if desired.

Bake: Bake 10–12 minutes, until edges are set and lightly golden and centers still look slightly underdone. If needed, rotate pans halfway for even browning.

Finish: Immediately sprinkle with flaky salt. For rounder cookies, use a glass or round cutter to “scoot” edges into shape while warm. Cool on the sheet 5 minutes, then transfer to a rack.