Melt the chocolate and butter together over low heat in a saucepan or in the microwave. Let the mixture cool after melting.
½ cup unsalted butter, 1 ounce unsweetened chocolate
In a large mixing bowl, using a hand or stand mixer, beat the powdered sugar, vanilla, milk, and salt together on medium-low speed until the sugar has dissolved.
16 ounces powdered sugar, ½ teaspoon pure vanilla extract, ¼ cup milk, ¼ teaspoon kosher salt
Slowly add the melted butter/chocolate mixture and beat on low speed until well incorporated and smooth. If needed, add 1 teaspoon of milk at a time to reach desired consistency.
Cover and set frosting aside until thick and spreadable.
Pipe or use a knife to frost cake or cupcakes.