Prep the pan: Heat oven to 425°F (220°C). Line a 12-cup muffin tin with liners.
Make the cream cheese filling: In a small bowl, mix cream cheese, sugar, vanilla, and egg yolk until smooth.
Set aside.
Combine dry ingredients: In a large bowl, whisk flour, cocoa, sugar, baking powder, baking soda, and salt.
Combine wet ingredients: In another bowl, whisk eggs, buttermilk, oil, vanilla, vinegar, and food coloring until well blended.
Make the batter: Pour wet ingredients into dry. Stir with a spatula just until combined. A few small lumps are fine—do not overmix.
Fill the cups: Divide batter evenly among liners, filling each about 2/3 full.
Add the swirl: Spoon about 1 tablespoon of cream cheese mixture on top of each muffin.
Use a toothpick or knife to gently swirl it into the batter.
Bake high, then lower: Bake at 425°F (220°C) for 5 minutes, then reduce oven to 350°F (175°C) and bake another 12–15 minutes, until a toothpick inserted into the red velvet portion comes out clean.
Cool: Let muffins cool in the pan for 5 minutes, then transfer to a rack. The cream cheese sets as they cool.
Serve: Enjoy slightly warm or at room temperature. The flavor deepens after a few hours.