Special equipment: a kitchen blowtorch
Lift the One Bowl Brownies out of the pan using the overhanging foil. Use a 9-inch stainless steel bowl to cut out a circle; reserve the circle.
Completely line the same 9-inch bowl with plastic wrap, leaving a 6-inch overhang around the edge. Scoop the softened ice cream into the bowl and use a rubber spatula to smooth it down. Carefully lift the brownie round with a flat spatula and place on top of the ice cream. If it breaks, that's ok, just use the brownie pieces to fill in the gaps. Fold the plastic wrap over the top of the brownie and place in the freezer until solid, 4 hours. Place a marble slab in the freezer to chill. (If you don't have a marble slab, place a baking sheet lined with foil in the freezer; it works just as well.)
When ready to serve, place a small saucepan of water over medium heat and bring to a simmer. Add the egg whites to the bowl of a stand mixer, and then place the bowl over the simmering liquid, making sure the bottom of the bowl does not touch the hot water. Whisk until the egg whites are frothy, then add the sugar a tablespoon at a time, whisking well after each addition. Whisk in the cream of tartar. Keep whisking the eggs over the heat until the sugar has dissolved and the egg whites are warm, 2 to 3 minutes. Move the bowl to the stand mixer fitted with the whisk attachment. Beat until stiff, glossy peaks form, 8 to 10 minutes. Beat in the vanilla and mix until combined.
Remove the bowl with the ice cream from the freezer. Unwrap the top of the plastic wrap, pop the molded ice cream/brownie out of the bowl and place it brownie-side down on the chilled marble slab. Remove the plastic wrap. Completely cover the ice cream and brownie with the meringue, making sure to seal the edges on the chilled slab. Bring the baked Alaska out to your guests, set it on the table and use a kitchen torch to brown the meringue!
Preheat the oven to 325 degrees F; line a 13-by-9-inch cake pan with foil and leave a 2-inch overhang on all sides. Spray with nonstick spray.
Add the butter to a medium glass bowl and melt in the microwave. Add the cocoa, granulated sugar and brown sugar, and stir vigorously until the mixture is smooth. Stir in the eggs one at a time, stirring well until mixed in completely after each addition. Add the flour, salt and vanilla extract and again stir vigorously until the batter is well combined.
Pour the batter into the prepared pan and smooth down and even the top. Bake until a cake tester inserted in the center of the brownie comes out clean with just a few crumbs, 30 minutes. Let cool completely.
Propane gas torches are highly flammable and should be kept away from heat, open flame and prolonged exposure to sunlight. They should be used only in well-ventilated areas. Follow torch manufacturer's instructions for use.