Preheat the oven to 350°F (175°C). Grease a mini muffin pan with nonstick cooking spray and set aside.
In a small mixing bowl, whisk together the flour and unsweetened cocoa powder. Set aside.
In a medium-sized mixing bowl, combine the melted butter, sugar, red food coloring, vanilla extract, and eggs. Stir until well mixed.
Gradually stir in the flour mixture, making sure not to overmix.
In another medium-sized mixing bowl, beat the cream cheese using a handheld mixer at medium-high speed for 1 minute.
Add the sugar and vanilla extract to the cream cheese, and mix for another 1-1½ minutes until fully combined.
Add the egg yolk to the cream cheese mixture, and mix just until no yellow streaks remain.
Transfer the cheesecake mixture into a disposable piping bag or a quart-size ziplock bag.
Add 1 tablespoon of the red velvet base to each mini muffin cavity in the prepared pan.
Snip off the end of the piping bag or ziplock bag, and pipe about 2 teaspoons of cheesecake filling into the center of each red velvet base.
Bake for 8-9 minutes. Remove from the oven and allow the mini cheesecakes to cool in the pan for 20-30 minutes before transferring them to a wire rack to cool completely.