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 yogurt 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.
*I suggest using unsweetened cocoa powder rather than Dutch-processed because it lets more of the red color come through on the swirl.**Disclaimer: I'm not a nutritionist. Nutrition facts are estimates.