Preheat oven: Set oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper or lightly grease it.
Make red velvet base: In a mixing bowl, combine melted butter and sugar. Beat in eggs, vanilla, and red food coloring. Stir in cocoa powder, flour, and salt until just combined. Reserve about 1/4 cup of batter for swirling. Spread the rest evenly in the prepared pan.
Make cheesecake layer: In another bowl, beat together cream cheese, sugar, egg, and vanilla until smooth. Pour over the red velvet layer.
Swirl: Dollop the reserved red velvet batter on top and use a knife or toothpick to create swirls.
Bake: Bake for 30–35 minutes, or until the center is set and a toothpick comes out mostly clean. Let cool completely before slicing.
Chill (optional): For cleaner cuts and an extra fudgy texture, chill in the fridge for 1–2 hours before serving.