1. 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.

2. 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.

3. 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.

4. 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.

5. Serve the cakes with hot fudge sauce and espresso ice cream.