With a handheld mixer or in the bowl of a stand mixer, mix butter until light and creamy, 1-2 minutes. Add powdered sugar. Sift cocoa powder into the bowl. Add salt, vanilla and 2 Tbsp milk. 

Mix on low speed, scraping down sides of bowl as needed, until ingredients are mostly combined. Add 1-2 Tbsp of remaining milk, increase speed to medium, and continue mixing for 1-2 minutes until frosting is creamy and fluffy, scraping down the sides of the bowl as needed. Add additional milk for softer frosting, or add more powdered sugar for thicker frosting.

Press through the frosting with a silicone spatula to get rid of air bubbles, if needed. Use the frosting immediately (this is preferred), or store in refrigerator, covered, for several days. If using out of the refrigerator, add 1-2 tsp milk and beat with a mixer until creamy.