Brown the butter in the oven. Preheat the oven to 325°F. Place the butter in a light-colored, oven-safe baking dish. Bake uncovered until melted, then continue baking, carefully stirring or swirling about every 8–10 minutes. As the water evaporates, the butter will foam and the milk solids will begin to toast. Once browning begins, check more frequently. Remove when the milk solids are deep golden to amber and the butter smells distinctly nutty and toasted, approximately 30–45 minutes.

Save the browned milk solids. Immediately scrape the brown butter—and every flavorful brown speck—into a heat-safe mixing bowl. Do not strain. Those toasted milk solids carry much of the brown-butter flavor.

Cool to a soft-solid consistency. Cool at room temperature for about 15–20 minutes, then refrigerate until the butter becomes opaque, soft-solid and spreadable. Stir once or twice as it cools to redistribute the browned milk solids. The texture should resemble softened butter, not melted butter and not refrigerator-hard butter.

Cream the butter and sugars. Increase the oven temperature to 350°F. Beat the cooled brown butter, brown sugar and granulated sugar together for about 2–3 minutes, until thoroughly combined and slightly lighter in texture. Brown butter contains less water than regular butter, so it will not become quite as fluffy.

Add the egg, yolk and vanilla. Beat in the whole egg until incorporated. Add the egg yolk and vanilla and mix until smooth, scraping down the bowl as needed.

Combine the dry ingredients. In a separate bowl, whisk together the flour, baking soda, baking powder and kosher salt.

Make the dough. Add the dry ingredients to the butter mixture and mix on low just until no dry flour remains. Do not overmix.

Fold in the chocolate. Fold in the chocolate chips or chopped chocolate. Reserve a small handful for pressing into the tops, if desired.

Chill the dough. Cover and refrigerate for at least 30 minutes. This allows the flour to hydrate and the butterfat to firm, helping control spread.

Portion. Line baking sheets with parchment paper. Portion the dough into approximately 2-tablespoon mounds and space about 2 inches apart. Press reserved chocolate pieces onto the tops, if desired.

Bake. Bake at 350°F for 10–12 minutes, until the edges are golden and set but the centers still look slightly soft. Do not wait for the centers to look completely baked; they will continue setting on the hot pan.

Cool and finish. Let the cookies rest on the baking sheet for 5 minutes, then transfer to a cooling rack. Finish with a light sprinkle of flaky sea salt while warm, if desired.