Melt the butter in a saucepan over medium heat. Stir and swirl occasionally until it foams, then turns golden brown and smells nutty. Scrape all the browned bits into a large mixing bowl. Let it cool for 10–15 minutes.

Add brown sugar and granulated sugar to the brown butter and whisk to combine.

Add the egg, egg yolk, and vanilla extract and whisk until smooth and glossy.

Stir in the sourdough discard until fully incorporated.

Add the dry ingredients to the wet ingredients and stir with a spatula or wooden spoon until just combined. Fold in the chocolate chips or chunks.

Cover and refrigerate the dough for at least 2 hours or up to 72 hours. Chilling is essential for thicker, more flavorful cookies.

When ready to bake, preheat oven to 350°F and line baking sheets with parchment paper. Scoop dough into 2-tablespoon-sized balls and place 2 inches apart.

Bake for 10–12 minutes or until the edges are golden and the centers still look slightly soft.

Immediately after baking, press extra chocolate chips on top and use a large round cookie cutter or glass to gently "scoot" the cookies into perfect circles, if desired.

Cool on the baking sheet for 5 minutes, then transfer to a wire rack. Sprinkle with flaky sea salt if using. Allow to cool completely.