1 cup white sugar
1/4 cup unsweetened cocoa powder
1 ounce red food coloring
1 teaspoon vanilla extract
1 teaspoon distilled white vinegar
1/4 teaspoon salt
2 large eggs, slightly beaten
3/4 cup all-purpose flour
1 (8 ounce) package cream cheese at room temperature
1/4 cup white sugar
1 large egg
1/4 teaspoon vanilla extract
Preheat oven to 350 degrees F (175 degrees C). Grease an 8x8-inch baking pan. Whisk melted butter with 1 cup sugar in a large mixing bowl; stir cocoa, red food coloring, 1 teaspoon vanilla extract, vinegar, and salt into butter mixture one at a time, mixing well after each addition to avoid lumps. Stir 2 eggs into mixture until thoroughly combined. Stir flour into cocoa mixture just until combined; set aside 1/4 cup batter. Pour remaining batter into the prepared baking dish. Beat cream cheese in a bowl using an electric mixer on medium speed until light and fluffy; beat 1/4 cup sugar, 1 egg, and 1/4 teaspoon vanilla extract into cream cheese until very well blended and only small lumps remain, 3 to 4 minutes. Spoon cream cheese mixture in dollops over the batter in pan; gently smooth tops of dollops even with batter using a knife or offset spatula. Do not overmix. Drizzle reserved 1/4 cup of batter over the dollops of cream cheese mixture. Drag a knife or skewer through the batter and cream cheese mixture to create swirls. Bake in the preheated oven until a toothpick inserted into the center of the pan comes out clean, 30 to 35 minutes. Cool completely before cutting into bars; store covered in refrigerator.