Combine the sugar, egg whites, and salt in the bowl of your stand mixer. Set bowl over a saucepan filled with 1-inch of gently simmering water. Whisking constantly until sugar is dissolved and mixture is thicker and foamy and reaches 150°F.
Using a stand mixer with a whisk attachment, beat the egg white mixture on medium speed until slightly cooled and thickened, about 2 minutes. Add butter, 1 tablespoon piece at a time, until smooth and creamy. If the frosting becomes too warm and greasy, refrigerate the bowl for 10 to 15 minutes then continue to beat until smooth.
Add chocolate and vanilla extract and mix until combined. Increase speed to medium-high and beat until light, fluffy, and well combined.
Frost cake when cooled, add sprinkles, and enjoy!