In the bowl of a stand mixer using the paddle attachment, cream the butter and vanilla on medium-high speed for about 1.5 minutes until smooth.
Reduce the mixer speed to low and gradually add 2 cups of powdered sugar. Allow it to blend in, then increase the speed to medium-high and mix for about until everything is incorporated.
Scrape down the sides of the bowl with silicone spatula, add 1 tablespoon of milk, and blend again until smooth.
Add the remaining 2 cups of powdered sugar, starting on low speed to avoid a sugar cloud. Once incorporated, increase the speed to medium-high.
Add another tablespoon of milk and scrape down the sides of the bowl again. Blend on medium-high speed until the frosting is light and fluffy.
If the frosting is too thick, add the remaining tablespoon of milk, a little at a time, until you reach your desired consistency.
Your buttercream frosting is now ready to spread or pipe onto your favorite sugar cookies!