Preheat the oven to 350°F (177°C). Spray an 8-inch square baking pan with nonstick spray. Set aside.

In a small bowl, beat the 2 eggs together. Set aside. Melt the butter in a large microwave safe bowl in 30 second increments until melted. Stir in 1 cup sugar, 2 teaspoons vanilla extract, cocoa powder, salt, food coloring, and vinegar. Mix each of those ingredients into the batter in that order. Whisk in the eggs, then fold in the flour until completely incorporated. Do not overmix. Pour the brownie batter into prepared baking pan, leaving about 3-4 Tablespoons for the top.

With a handheld mixer on medium speed, beat the softened cream cheese, 1/4 cup sugar, egg yolk, and 1/2 teaspoon vanilla in a medium bowl until completely smooth—about 1 minute. Dollop spoonfuls of the cream cheese mixture on top of the prepared brownie batter. Cover with the last few Tablespoons of brownie batter. Glide a knife through the layers as best you can (both layers are pretty thick), creating a swirl pattern.

Bake the brownies for 28-30 minutes or until a toothpick inserted in the middle comes out clean. Allow the brownies to cool completely before cutting into squares. Cover brownies and store at room temperature for 3 days or in the refrigerator for up to 6 days.