1. Prepare Your Baking Pan: Begin by preheating your oven to 350 F (175 C). Lightly grease an 8×8 inch baking pan with butter or cooking spray. For easier removal, you can also line the pan with parchment paper, leaving an overhang on the sides.

2. Combine Wet Ingredients: In a large mixing bowl, whisk together the melted butter and granulated sugar until well combined and smooth. This step helps create a uniform texture.

3. Add Eggs and Vanilla: Beat in the two large eggs one at a time, mixing well after each addition until fully incorporated. Stir in the vanilla extract. The mixture should become light and slightly fluffy.

4. Incorporate Sourdough Discard: Gently fold in the 1/2 cup of unfed sourdough discard. Mix until just combined; avoid overmixing at this stage. The discard will integrate smoothly into the wet ingredients.

5. Mix Dry Ingredients: In a separate medium bowl, whisk together the all-purpose flour, unsweetened cocoa powder, and salt. Ensure there are no lumps in the cocoa powder.

6. Combine Wet and Dry: Gradually add the dry ingredient mixture to the wet ingredients, mixing until just combined. Be careful not to overmix the batter; overmixing can lead to tougher brownies. A few streaks of flour are fine, as they will disappear during baking.

7. Fold in Chocolate Chips (Optional): If using, gently fold in the 1/2 cup of chocolate chips. This adds extra pockets of melted chocolate throughout the brownies.

8. Bake the Brownies: Pour the batter into your prepared 8×8 inch baking pan and spread it evenly. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out with moist crumbs, but not wet batter. The edges should look set.

9. Cool Before Slicing: Let the brownies cool completely in the pan on a wire rack before slicing. This is crucial for achieving that perfect fudgy texture and clean cuts. Cutting them while warm can make them fall apart.