In a saucepan, add about 1 inch of water, Bring it to a simmer.
In the stand mixer bowl, add the egg whites and granulated sugar. Place it on top of the saucepan with the simmering water. Make sure the water isn't touching the bowl otherwise you'll have scrambled egg whites.
Whisk until the sugar is dissolved and the egg whites reach 160 degrees.
Place the mixing bowl on the stand mixer fitted with the whisk attachment. Beat on medium/low for about 10 - 15 minutes until the egg whites have cooled to room temperature. Turn the mixer to high and beat until the meringue reaches stiff peaks. The meringue will be thick and shiny. If you turn the whisk upside down and the peak stands straight up, you've reached the stiff peak stage.
Swap out the whisk attachment for the paddle attachment. Add in the sifted powdered sugar and vanilla extract. Mix until combined.
Add all at once the shortening and cubes of butter. Beat until it all comes together. It will thicken up at this point. If the mixture looks like it curdled, keep mixing. It will come back together.
The frosting should be thick and creamy. If it looks separated, keep mixing. It will come back together.
You can also use a double boiler to heat the egg whites and sugar instead of the mixing bowl and saucepan.