Preheat the oven to 350°F. Grease a 9x13-inch baking pan or line it with parchment paper.

In a large mixing bowl, combine the melted butter and sugar. Whisk until well blended.

Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.

In another bowl, whisk together the flour, cocoa powder, baking powder, and salt.

Gradually add the dry ingredients to the wet mixture, stirring until just combined. Mix in the red food coloring until evenly distributed.

Pour half of the red velvet batter into the prepared baking pan, spreading it evenly.

In a separate bowl, beat the softened cream cheese and sugar until smooth. Add the egg and vanilla extract, mixing until well combined.

Spread the cheesecake mixture over the red velvet layer in the pan.

Spoon the remaining red velvet batter over the cheesecake layer, using a knife or toothpick to swirl the two layers together for a marbled effect.

Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool in the pan before cutting into squares.