Preheat your oven to 350°F (175°C). Line an 8x8 inch baking pan with parchment paper, leaving an overhang on two sides to easily lift the brownies out later. Lightly grease the pan and parchment.

In a medium bowl, use an electric hand mixer to beat the softened cream cheese and 1/4 cup of granulated sugar on medium speed until completely smooth and creamy, with no lumps.

Add the egg yolk and 1/2 tsp of vanilla extract. Beat on low speed until just combined. Be careful not to overmix. Set the cheesecake mixture aside.

In a large bowl, whisk together the melted butter and 1 cup of granulated sugar until well combined.

Add the eggs one at a time, whisking well after each addition until the mixture is glossy. Whisk in the vanilla extract, white vinegar, and red gel food coloring until the color is vibrant and uniform.

In a separate bowl, whisk together the all-purpose flour, cocoa powder, baking powder, and salt.

Gently fold the dry ingredients into the wet ingredients using a spatula until just combined. Do not overmix; a few streaks of flour are okay.

Reserve about 1/2 cup of the brownie batter. Pour the rest of the batter into the prepared baking pan and spread it into an even layer.

Drop spoonfuls of the cheesecake mixture evenly over the top of the brownie batter.

Dollop the reserved 1/2 cup of brownie batter over the cheesecake layer.

Use a butter knife or a skewer to gently swirl the batters together. Create a marbled effect, but don't overmix or the colors will become muddy.

Bake for 30-35 minutes, or until the edges are set and a toothpick inserted into the center comes out with moist, fudgy crumbs, but not wet batter. The cheesecake parts should be set and not jiggly.

Let the brownies cool completely in the pan on a wire rack for at least 2 hours. For the cleanest cuts, chill in the refrigerator for another 1-2 hours before slicing.