01 - Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper, ensuring the paper overhangs the edges for easy removal.
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 pale and slightly thickened.
03 - Sift cocoa powder, flour, salt, and baking powder directly into the wet mixture. Gently fold using a spatula until just combined, being careful not to overmix.
04 - Blend cottage cheese in a food processor or with an immersion blender until completely smooth. Add egg yolk, sugar, and vanilla; process until creamy and uniform in texture.
05 - Pour brownie batter into the prepared pan, spreading evenly with a spatula. Drop spoonfuls of the cottage cheese mixture over the batter in a grid pattern.
06 - Run a knife or skewer through the batter in a swirling motion to marble the two mixtures together, being careful not to over-blend.
07 - Bake for 33 to 36 minutes, until edges are set and a toothpick inserted in the center emerges with a few moist crumbs. The center should still feel slightly soft.
08 - Allow brownies to cool completely in the pan before lifting out by the parchment paper edges. Slice into 12 even squares for clean, professional cuts.