Preheat oven to 375 degrees F (190 degrees C). Grease a 12-cup muffin tin or line cups with paper liners.

Combine 9 tablespoons butter, white sugar, and vanilla extract in a large bowl; beat with an electric mixer until smooth and creamy. Add eggs one at a time and beat until well combined. Fold in half the flour and 1/4 cup milk and stir to combine. Repeat with remaining flour and milk. Spoon batter into the prepared muffin cups, filling each 3/4 full.

Bake in the preheated oven until a toothpick inserted in the center comes out clean, about 18 minutes.

Remove tin from oven and cool on a wire rack for 5 minutes. Remove cupcakes from the tin and cool completely on a wire rack before decorating, about 1 hour.

In a large bowl, mix powdered sugar and cocoa powder together; set aside.

In the bowl of your mixer, beat butter, vanilla, and cream on medium low speed until smooth and combined.

Decrease mixer speed to low and slowly add powdered sugar mixture, beating on low until barely mixed. Increase speed to high and beat for about a minute and a half, until smooth, light and fluffy. A butter knife should easily move through frosting -- if too thick, add cream, 2 tablespoons at a time until desired consistency is reached.