Set up a double boiler or make one using a bowl and a pan with about 1 inch of warm water. The bowl should sit above the water without touching it.
Add egg whites, sugar, and cream of tartar to the bowl. Place the bowl over the warm water.
On low heat, stir the egg white mixture constantly until gently warmed and the sugar is dissolved. Be careful not to cook the egg whites. Scrape the sides of the bowl and stir constantly.
Once the sugar is dissolved, whip the egg whites on high speed until stiff peaks form. The mixture should be glossy and thick. When the whisk is lifted, it should create a peak. Add the vanilla at this point.
Top the cooled brownies with the marshmallow icing. Use a blowtorch to toast the marshmallow topping for a true s'mores taste. If you don't have a blowtorch, place the brownies under the broiler for 1-2 minutes until golden brown, keeping a close eye on them.