Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, ensuring there's an overhang on the sides. This will make it easier to lift the cooled brownies out of the pan. Lightly grease the parchment paper.

In a medium saucepan or a microwave-safe bowl, melt the unsalted butter. Remove from heat and stir in the 1 1/2 cups granulated sugar until well combined. Allow the mixture to cool slightly for about 5 minutes.

Transfer the butter-sugar mixture to a large mixing bowl. Whisk in the 2 large eggs, one at a time, until fully incorporated and the mixture is smooth. Stir in 1 teaspoon of vanilla extract.

In a separate medium bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking powder, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing gently with a rubber spatula until just combined. Be careful not to overmix, as this can lead to tough brownies. If desired, fold in the 1/2 cup semi-sweet chocolate chips for an extra chocolatey punch.

In a food processor or blender, combine the 1 cup full-fat cottage cheese, 1 large egg yolk, 2 tablespoons granulated sugar, and 1/2 teaspoon vanilla extract. Process on high until the mixture is completely smooth and creamy, with no cottage cheese curds visible.

Spread about two-thirds of the brownie batter evenly into the prepared baking pan. Dollop spoonfuls of the smooth cottage cheese mixture over the brownie batter. Then, drop the remaining brownie batter in spoonfuls over the cottage cheese mixture.

Using a knife or a skewer, gently swirl the cottage cheese mixture into the brownie batter to create a beautiful marbled effect. Try not to over-swirl to maintain distinct layers.

Bake for 30-35 minutes, or until a toothpick inserted into the center (making sure to avoid the cottage cheese swirls) comes out with moist crumbs, but no wet batter. The edges should be set, and the center may still look slightly soft and fudgy.

Allow the brownies to cool completely in the pan on a wire rack before attempting to lift them out using the parchment paper overhang. Cooling completely is essential for achieving a perfectly fudgy and set texture. Once cool, cut into 12 squares and serve.