Use a hand mixer or stand mixer to whip the softened butter until it is very smooth and creamy.
1/2 cup unsalted butter
Add 3 cups of the powdered sugar, and beat until combined. You can add more sugar if want it sweeter.
3-4 cups powdered sugar
With the hand mixer or stand mixer running, pour the vanilla and milk into the frosting. Beat until the frosting is smooth and the desired consistency.
1 teaspoon vanilla extract, 3 Tablespoons milk
Taste the frosting and adjust as necessary. Add more sugar to make the frosting sweeter or thicker. Add more milk to make it thinner.
Notes
Leftovers can be stored in an airtight container in the fridge for 2 weeks, or in the freezer for 6 months.
To use leftovers, let the frosting thaw for 3 hours if refrigerated, or 6 hours if frozen. Then mix with a hand mixer or stand mixer until the desired consistency.
For a creamier frosting, use whipping cream instead of milk.
You can spread the buttercream on cake with a knife or spatula, or use a piping bag.