In a stand mixer bowl, with the mixer on medium speed, whip the butter for 2 minutes until it is almost white in color.
Add in the powdered sugar, vanilla and 3 tablespoons milk. Beat on low speed for 2-3 minutes, adding in the last tablespoon of milk if the buttercream needs to be thinner.
Notes
*I usually use heavy cream. If the milk has a higher fat content (such as heavy cream as compared to 2% milk), you may need to add more because it is thicker.