Begin by melting the chocolate. Place the chopped chocolate in a heat-safe bowl and set it over a pan of gently simmering water to create a double boiler; stir until the chocolate is completely smooth and melted. Alternatively, melt the chocolate in the microwave, heating it in 30-second intervals and mixing thoroughly between each interval. Once the chocolate is fully melted, remove the bowl from the heat and set it aside to cool slightly.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a handheld mixer, beat the butter on medium speed until creamy, about 1 minute. Add the sugar, vanilla, milk, and salt. Beat on low speed for 30 seconds, then increase speed to medium-high, and beat for 2 full minutes.
Add the melted chocolate, and beat the mixture on high speed for another 1 to 2 minutes, until the frosting is fluffy and the ingredients are completely combined. Add more powdered sugar if the frosting is too thin, more milk if the frosting is too thick, or an extra pinch of salt if the frosting is too sweet. The frosting should be soft and creamy, but not runny.