Melt chocolate: Place your chopped chocolate in a microwave-safe bowl and microwave for 30 seconds. Stir well. Return the chocolate to the microwave and heat for another 15 seconds, and stir again. Continue heating the chocolate for 15 seconds, stirring after each, until the chocolate is completely melted and smooth.
Using an electric hand mixer or a stand mixer on medium speed, beat in a large bowl the unsalted butter until smooth and creamy, about 3 - 4 minutes.
Add melted chocolate, vanilla extract, and salt. Mix until well combined.
Reduce mixer speed to low, add 1 cup of confectioners’ sugar and keep mixing until incorporated. Once incorporated, add the remaining confectioners’ sugar; beat on low speed for 1 minute, then increase the speed to medium-high and beat for 4 - 5 minutes until the frosting is smooth, scraping down the bowl once or twice.
Add the milk, one tablespoon at a time, and keep mixing to incorporate for 4 - 5 minutes until the frosting is smooth, fluffy, and spreadable, scraping down the bowl once or twice (read recipe notes). NOTE: The frosting should be soft and spreadable, but not runny. If the buttercream is too thick, beat in more milk, 1 tablespoon at a time, until the desired consistency is reached. If it is too thin, add more confectioners’ sugar, 1/4 cup at a time, until the desired consistency is reached
Before using, mix the frosting by hand with a wooden spoon or large spatula to push out the air pockets to create a silky-smooth frosting.