Make cupcakes: Preheat oven to 350°F. Place paper liners in a 12-cup muffin tin and 4 cups of a 6-cup muffin tin. Fill 2 empty muffin cups halfway with water.
Mix flour, cocoa, salt and baking powder. In a separate bowl, with an electric mixer, beat butter until creamy. Gradually add sugar and beat until light and fluffy. Add eggs, one a time, beating well after each addition. Beat in yolks, food coloring and vanilla. Alternate adding dry ingredients and milk, beginning and ending with dry ingredients. Beat just until all ingredients are incorporated.
Divide batter among cupcake liners. Bake until a toothpick inserted into center of a cupcake comes out clean, about 20 minutes. Cool in pans on wire rack for 10 minutes, then remove cupcakes from pans to rack to cool completely.
Make frosting: Using an electric mixer on medium speed, beat cream cheese and butter until smooth. Beat in vanilla. Gradually add sugar and beat until easy to spread.