Preheat oven to 350°F (175°C). Grease and flour a Bundt pan thoroughly to prevent sticking.
Beat cream cheese until smooth. Add sugar, egg, and vanilla; mix until creamy. Set aside.
Sift flour, cocoa, baking soda, and salt.
In a separate bowl, cream butter and sugar until fluffy. Beat in eggs one at a time, then add vanilla, vinegar, and red food coloring.
Add dry ingredients and buttermilk in three parts, starting and ending with dry mix. Stir just until combined.
Pour half the batter into the pan.
Spoon cheesecake filling in the center, avoiding edges. Cover with remaining batter and smooth the top.
Bake for 50–60 minutes. A toothpick in the red velvet should come out clean. Cool in pan 15–20 minutes, then invert and cool fully.
Glaze (Optional): Beat cream cheese and butter until smooth. Add powdered sugar, vanilla, and enough milk for a pourable glaze. Drizzle over cooled cake.