01 - Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper, ensuring the paper overhangs the sides for easy removal later.
02 - In a large bowl, whisk melted butter and granulated sugar until smooth and well incorporated. Add eggs and vanilla extract, whisking until the mixture is glossy and thoroughly combined.
03 - Sift cocoa powder, all-purpose flour, salt, and baking powder directly into the wet ingredients. Mix gently with a spatula just until combined; do not overmix to maintain a tender texture.
04 - In a separate bowl, blend cottage cheese using a food processor or immersion blender until completely smooth and creamy. Add egg yolk, granulated sugar, and vanilla extract; blend until fully incorporated and no lumps remain.
05 - Pour brownie batter into the prepared pan, spreading evenly with a spatula to create a smooth surface. Spoon dollops of the cottage cheese mixture over the batter, distributing evenly across the top.
06 - Using a knife or skewer, gently swirl the cottage cheese mixture into the brownie batter in a figure-eight or circular motion. Take care not to overmix; you want distinct marbled patterns, not a fully blended batter.
07 - Bake for 33 to 36 minutes, or until the edges are set and slightly pulling away from the pan sides. A toothpick inserted into the center should emerge with a few moist crumbs but not wet batter.
08 - Allow brownies to cool completely in the pan before slicing. This step is crucial as the brownies continue to set and the flavors develop during cooling. Lift out using the parchment paper overhang and cut into 12 equal squares.