Prepare the Baking Dish: Preheat the oven to 350°F (175°C). Line a 9 × 13-inch baking dish with parchment paper to prepare it for the batter.
Combine the Butter and Sugars: Melt the unsalted butter in a large mixing bowl. Add the packed brown sugar and granulated sugar, then mix until well combined.
Add the Eggs and Vanilla: Mix the room-temperature eggs and egg yolk into the butter-sugar mixture. Add the vanilla extract and stir until evenly incorporated.
Mix the Dry Ingredients: Sift the all-purpose flour into a separate bowl. Add the cornstarch, baking powder, and salt, then whisk to distribute the ingredients evenly.
Combine the Batter: Gradually add the dry ingredients to the butter-sugar mixture. Stir gently until the flour is just incorporated, taking care not to overmix.
Fold in the Butterscotch Chips and Walnuts: Add the butterscotch chips and, if desired, the chopped walnuts. Fold them into the batter until distributed throughout.
Transfer the Batter to the Dish: Spread the batter evenly in the prepared baking dish, reaching the edges so the brownies bake in a consistent layer.
Bake the Brownies: Place the dish in the preheated oven and bake for 25–28 minutes, until the brownies are baked through.
Add the Finishing Chips: Remove the baking dish from the oven and sprinkle a few extra butterscotch chips over the top while the brownies are still hot.
Cool and Slice: Allow the brownies to cool before cutting them into squares with a plastic knife. Serve and enjoy.