In the bowl of a stand mixer fixed with the paddle attachment, whip the softened butter on medium-high speed until light and fluffy, 3 minutes. Scrape down the sides of the bowl.
In a separate bowl, whisk together the powdered sugar and Dutch-processed cocoa powder. Pour half of the dry ingredients over the whipped butter and mix on low speed for 30 seconds, then increase the speed to medium-high and mix for another 3-4 minutes, scraping down the sides of the bowl every minute.
Add in the remaining dry ingredients, milk, vanilla extract, and salt, and repeat the same mixing procedure as above for another 2-3 minutes, until the mixture is fluffy and homogenous.