Preheat oven to 325 degrees. Using a stand mixer with the paddle attachment, beat the butter and shortening at medium speed until creamy. Gradually add the sugar and beat until light and fluffy.
Add eggs 1 at a time, beating just until each one is incorporated.
Stir together flour, baking powder, and salt.
Add flour mixture to butter mixture alternating with milk, beginning and ending with flour.
Stir in vanilla.
Measure out 2 1/2 cups of batter and transfer to a medium bowl. Stir in cocoa powder and red food coloring.
Grease and flour a 10-inch Bundt pan or spray with baking spray. Spoon enough uncolored batter into the Bundt pan to just cover the bottom of the pan.
Spoon about half of the red batter into the bundt pan.
Spoon about half the remaining uncolored batter into the pan followed by the rest of the red batter. Finish off with the remaining uncolored batter.
Bake for 60 to 65 minutes, or until a toothpick inserted in the center comes out clean. Cool in pan for 10 minutes and then invert onto a cake stand or serving platter. Cool completely before glazing.
To make glaze, whisk together all ingredients in a bowl. Add a touch more milk if too thick. Drizzle on top of cake.