Preheat oven to 350 F. Grease and flour a 10-15-cup bundt pan.
In a medium bowl, whisk together cake flour, baking powder, and salt.
In the bowl of a stand mixer fitted with a paddle attachment, beat together butter, sugar, and sour cream until well-combined.
Stir in vanilla until combined.
Add eggs one at time, mixing well after each addition.
On low, stir in flour mixture until just incorporated.
Stir in milk until combined.
In a separate large bowl, stir together 2 ½ cups of the batter, cocoa powder, milk, and red food coloring until well-combined.
Using a 1/4-cup measuring cup, drop two scoops of plain batter into prepared bundt pan.
Drop one scoop of red velvet swirl batter on top of plain batter.
Continue to alternate between plain and red velvet swirl batters until both batters are gone.
Bake for 50-60 minutes, or until a wooden toothpick inserted into the center comes out clean.
Cool cake in the pan on a wire rack for 15 minutes.
Invert the cake onto wire rack, and cool completely.
Video
Notes
Cake flour - Cake flour helps to give the cake its tender crumb. If you don't have cake flour, you can make a substitute with this recipe.
Butter - I use salted butter. If using unsalted butter, increase the salt by 1/2 teaspoon.
Sour cream - Full-fat sour cream, whole milk Greek yogurt, 2% yogurt, or plain nonfat Greek yogurt will all work.
Milk - I recommend using 2% or whole milk. The fat helps to make the cake moist.
Unsweetened cocoa powder - I suggest using unsweetened cocoa powder rather than Dutch-processed because it lets more of the red color come through on the swirl.