01 - Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper, ensuring paper overhangs edges for easy removal.
02 - Whisk melted butter and granulated sugar in a large bowl until smooth. Add eggs and vanilla extract, whisking until fully incorporated and glossy.
03 - Sift cocoa powder, flour, salt, and baking powder into the wet mixture. Fold gently with 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.
05 - Spread brownie batter evenly in the prepared pan. Drop spoonfuls of cottage cheese mixture over the surface. Run a knife or skewer through the batters in a figure-eight pattern to create marble effect.
06 - Bake for 33 to 36 minutes until edges are set and a toothpick inserted in the center comes out with moist crumbs. The center should still appear slightly fudgy.
07 - Allow brownies to cool completely in the pan before lifting out by parchment paper edges. Slice into 12 squares for clean cuts.