Brown the Butter: Melt butter over medium heat until it turns golden brown and smells nutty (5–7 minutes). Transfer to a bowl and let cool for 30 minutes.
Mix Wet Ingredients: In a large bowl, whisk the cooled butter with both sugars. Add the egg, vanilla, and sourdough discard, mixing until smooth.
Combine Dry Ingredients: In another bowl, whisk flour, baking soda, and salt.
Make the Dough: Add dry ingredients to wet, mixing gently until just combined. Stir in chocolate chips. The dough may be sticky.
Chill: Cover and refrigerate for at least 2 hours (or overnight for more flavor).
Preheat Oven: Heat oven to 350°F (180°C) and line baking sheets with parchment.
Shape Cookies: Scoop about 1.5 tablespoons of dough per cookie, roll into balls, and place 2 inches apart.
Bake: Bake 10–12 minutes, until the edges are golden but centers still look soft.
Cool: Let rest on the baking sheet for 5 minutes, then transfer to a wire rack.