Meanwhile prepare your frosting. In the bowl of a standing mixer, thoroughly whisk together sugar and egg whites.
Set the bowl over a pot of boiling water. Whisking constantly, heat the mixture for 1.5 minutes. Don't ever stop whisking or you will have scrambled eggs. Remove from heat.
Place bowl back in the mixer fitted with a whisk attachment. Beat on high speed until mixture forms a stiff meringue and the bowl comes to room temperature, 10-20 minutes.
Stop the mixer and replace the whisk attachment with the paddle attachment.
Set mixer to low and add the butter. When all of the butter is incorporated, turn the mixer to medium and beat until fluffy. Turn mixer down to low and add vanilla. Mix until smooth and creamy.
Buttercream troubleshooting: If the buttercream is soupy or too liquidy after combining the butter and vanilla, don't worry. It just needs to be chilled for a bit. Try putting it in the refrigerator for 30 minutes to an hour. Then beat it on high again until fluffy and glossy. It should have a slight sheen to it. It's beautiful frosting!
Buttercream storage tips: Serve immediately or store in an airtight container for 2 days at room temperature or 10 days in the refrigerator.