Preheat the oven to 350 degrees. In the bowl of a stand mixer fitted with a whisk attachment, beat egg whites and sugar on medium speed until foamy; add cream of tartar. Increase speed to high; beat egg whites until tripled in volume, stiff, and glossy. Transfer egg white mixture to a large bowl; fold in flour in three additions.
Transfer batter to a piping bag fitted with a 1/2-inch to 3/4-inch round tip and pipe into ungreased mini angel food cake pans with removable bottoms. Smooth tops with an offset spatula. Run a knife through batter to pop air pockets. Bake until cakes are golden in color and spring back when gently pressed, about 25 minutes.⏱ 25 min
Invert pans over the necks of glass bottles and allow cakes to cool, at least 1 hour. To remove cakes from pans, run a knife around sides and center tube of pans. Release cakes from sides and run a long knife along the bottom of the cakes, freeing them from the tube.⏱ 60 min
Make the hot fudge sauce: Combine all ingredients except the vanilla in a saucepan and cook over medium heat, stirring constantly, until the mixture comes to a full boil. Boil the mixture briskly for 3 minutes, stirring occasionally, then remove from the heat and stir in the vanilla.⏱ 3 min
Serve the cakes with hot fudge sauce and espresso ice cream.