Put your 5 egg whites, 1 cup + 2 tablespoons sugar and a pinch of salt in the bowl of your stand mixer (should be heatproof) and set that over a pan of simmering water. If you own a candy thermometer, clip that onto your bowl too.
Constantly whisk your mixture by hand until the temperature reaches 140F (see notes). While whisking, swipe the sides of your bowl with your whisk once in a while to make sure no sugar crystals form.
Take the bowl out of the heat and directly into your stand mixer fitted with the whisk attachment. Whisk on medium-high speed until you reach stiff peaks, the mixture is smooth and fluffy, and the bottom of your bowl is cool to the touch.
With the mixer on medium-low speed, start to gradually add the 2 cups butter, small parts at a time, mixing well after each addition. Remember to scrape the bottom and sides of your bowl.
Once you've added all the butter, add the 1½ teaspoons of vanilla and stir.
Switch to the paddle attachment and continue beating on medium-low speed until your buttercream becomes smooth, glossy and creamy.
No thermometer? No problem. If the mixture feels warm and if you don't feel any grains of sugar anymore when you rub a small amount between your fingers - you're good.
At some point your buttercream will look curdled and really quite awful. Don't worry. Just keep whipping.
I have no exact recipe for flavoured Swiss meringue buttercream. I just add whatever ingredient it is (e.g. melted chocolate or peanut butter) a little at a time until I get the flavour I want. Just make sure what you're adding is room temperature.
This yields about 4 cups of frosting. I've found that's just enough to frost and fill a 2-layer, 9-inch cake (but I'm a heavy froster so that's something to keep in mind).