In a stand mixer fitted with a paddle attachment, whip the butter on medium speed until creamy and light in color, about 4 minutes. Scrape down the bowl and paddle, then add half of the powdered sugar. Mix on low speed until just incorporated, then add the rest of the powdered sugar. With the mixer still in the off position, sift in the black cocoa powder and add the vanilla, milk, and salt. Mix on low until all ingredients are thoroughly combined, about 2 minutes, scraping down the bowl and paddle as needed.