In a stand mixer fitted with the paddle attachment (or a handheld mixer with an eggbeater or whisk attachment), beat butter on high speed until as pale as ivory and very fluffy, at least 5 minutes. Scrape sides and bottom of bowl twice while beating.
Turn the mixer to low and gradually add sugar. When combined, scrape bowl again, then slowly drizzle in milk, vanilla, and food coloring; mix until combined. Scrape bowl again.
Turn the mixer to high and beat the buttercream until extremely fluffy, 8 to 10 minutes. "It should look almost like whipped cream, and should lose the waxy sheen that butter has."
Make ahead: Up to 3 hours at room temperature. Although you can make buttercream a few days ahead and chill, it will take a while to return it to room temperature (about 3 hours) and re-whip to the proper cloudlike texture--much longer than just making it fresh.