Preheat the oven to 375°F. Lightly grease 2 mini cupcake pans, or a 9x9 pan.
Put all of the ingredients into a large bowl in the order in which they're written. Stir, then beat the mixture until it's smooth.
Spoon the batter into the prepared pan.
Bake the brownies for 10-12 minutes for mini brownies, or about 25 minutes (for the 9" pan) or until they're just barely beginning to pull away from the sides of the pan. A toothpick inserted into the center will come out clean or with a few moist crumbs clinging to it; you shouldn't see any wet batter.
Remove brownies from the cupcake pan after 10 minutes and let cool completely. Cut brownies in the pan after they are cooled.
For the frosting:
Cream together the butter and cream cheese and vanilla. Add the vanilla. Add the powdered sugar 1 cup at a time and mix for 3-4 minutes. Add milk to desired consistency. Pipe onto brownies.
Notes
Adapted from King Arthur Flour Fudge Brownie Recipe