Preheat the oven to 225° and position racks in the lower and middle thirds. Trace an 11-inch circle on the undersides of each of 2 sheets of parchment paper. Turn the paper over onto 2 large baking sheets.
In the bowl of a standing electric mixer fitted with the whisk, beat the egg whites with the cream of tartar at medium speed until foamy. Increase the speed to high and beat until soft peaks form. Add the granulated sugar 1 tablespoon at a time, beating for 5 seconds between additions. Add the vanilla and beat until the whites are stiff and glossy, about 4 minutes.
Transfer half of the meringue to a pastry bag fitted with a 1/2-inch plain round tip and pipe a ring of meringue just inside each drawn circle. Spoon the remaining meringue into the circles and spread it 1/2 inch thick. Bake the meringues for about 1 1/2 hours, until very pale but dry. Turn off the oven, prop the door open slightly and let the meringues cool in the oven for at least 6 hours, until dry and crisp.
In a bowl, using an electric mixer, beat 2 cups of the cream with the confectioners' sugar until firm. Fold in one-fourth of the chocolate. Spread the cream over 1 round, spreading it to the edge. Top with the second round, pressing it lightly. Freeze until the cream is firm, about 4 hours.
Meanwhile, melt the remaining chocolate in a bowl set over a pan of simmering water. Off the heat, whisk in the remaining 1/4 cup of cream and the espresso.
Using a serrated knife, cut the frozen cake into wedges and transfer to plates. Let stand for 10 minutes. Spoon some of the sauce on each wedge and serve.