Brown the butter. Melt 8 oz butter in a heavy saucepan over medium-low heat. Continue to cook, swirling occasionally, until butter becomes brown. It will pop and sputter a lot at first, but then it will quiet down. It's ready when the popping has calmed down, there are brown specks at the bottom of the pan, and it smells toasty and nutty. Pour into a large mixing bowl and set aside to cool for about 10 minutes.
Make the cookie dough. Add 1 cup brown sugar and ½ cup sugar to melted brown butter; whisk thoroughly.
Add 2 eggs, whisking in one at a time until fully incorporated. And 2 tsp vanilla; whisk mixture until homogenized and silky smooth. Whisk in ½ cup sourdough discard.
In a separate bowl, whisk together 2 ¼ cups flour, 1 tsp baking soda, and 1 ½ tsp salt. Add dry ingredients to butter mixture, folding with a spatula until about halfway combined, with streaks of flour remaining. Add 2 cups chocolate chips/chunks, folding in gently until just combined and no streaks of flour remain.
Chill. Rest cookie dough in the fridge for about 30 minutes. You can skip this step, but the cookies will spread more and turn out a bit different!
Bake. Preheat oven to 350° F and line a baking sheet with parchment paper. Scoop cookie dough using a large 3 tbsp scoop, leveling it off so it's even with the scoop. Place cookie dough balls about 2 inches apart on baking sheets (I always put 8 cookies on each sheet). Bake until golden around the edges and not quite set in the centers, about 9-11 minutes. Remove cookies from oven and allow to cool on the baking sheet for a minute or two before transferring to a cooling rack.