In a small saucepan, melt the butter over medium heat. Cook, swirling the pan occasionally, until the butter turns golden brown and smells nutty (about 4–5 minutes). Watch closely to avoid burning.
Pour the browned butter into a mixing bowl and let it cool slightly (5–10 minutes).
Add the brown sugar, granulated sugar, and sourdough discard to the browned butter. Whisk until smooth.
Mix in the egg yolk and vanilla extract until fully combined.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the chocolate chips, ensuring they’re evenly distributed throughout the dough.
Cover the bowl and refrigerate for at least 30 minutes (or up to 24 hours for enhanced flavor).
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Scoop dough out with a 2-inch cookie scoop and place them 2 inches apart on the baking sheet.
Bake for 10–12 minutes, or until the edges are golden brown and the centers look slightly underdone.
Remove from the oven and allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely. Enjoy with milk!