This recipe goes with Rainbow Layer Cake.
Cream butter with an electric mixer on medium-high speed in a large bowl. Beat in vanilla extract.
Add powdered sugar in three batches, adding milk as necessary and scraping the sides of the bowl between each batch. Mix on low speed until mostly combined, and medium speed until smooth.
Spread about 1/2 cup of frosting between each cake layer and use remaining frosting to cover the cake.