Preheat oven to 350°F. Line baking sheets with parchment paper and set aside.
Brown the butter: Melt 1 cup butter in a saucepan over medium heat, stirring often until golden brown and nutty-smelling. Pour the browned butter into a bowl to cool (do not keep in the pan or it may burn). Cool before using.
In a large mixing bowl, beat together the browned butter, 1 ¼ cups brown sugar, ½ cup granulated sugar, and ⅓ cup sourdough discard until smooth.
Add 3 large eggs and 3 teaspoons vanilla extract; mix well.
In another bowl, whisk together 3 cups all-purpose flour, 3 ounces vanilla instant pudding mix, 1 teaspoon baking soda, and 1 teaspoon salt. Gradually add to the wet ingredients and mix until combined.
Stir in 1 cup mini chocolate chips and 1 cup chocolate chunks.
Using a small cookie scoop, portion dough onto prepared baking sheets.
Bake for 10–12 minutes, or until the edges are lightly golden.
Let cookies cool on the baking sheet for 3 minutes, then transfer to a wire rack.
Sprinkle with sea salt if desired. Enjoy!