Beat 3 sticks softened butter and 1/4 teaspoon salt with a mixer on medium-high speed until fluffy, 2 minutes. Gradually beat in 1 1/2 cups confectioners’ sugar on low speed until combined.
Add 2 tablespoons unsweetened cocoa powder and 2 teaspoons vanilla and beat on medium-high speed until fluffy, about 3 minutes. Beat in 6 ounces cooled melted semisweet chocolate until smooth and fluffy, 2 to 3 more minutes.
Spread the frosting on the cake. Refrigerate 30 minutes before serving.