Moist cake is topped with three layers of ice cream and fluffy meringue in this old-fashioned dessert.
Preheat oven to 350 degrees. Line a 9-inch round cake pan with parchment paper, and spray with cooking spray.
Combine 3 tablespoons sugar and the egg yolks in bowl of an electric mixer fitted with the whisk attachment; whisk, on medium speed, until pale yellow and thick, about 15 minutes. Add vanilla, and fold in melted chocolate just to combine.
Combine egg white and a pinch of salt in bowl of electric mixer fitted with the whisk attachment; whip, on medium speed, until frothy. Add remaining 3 tablespoons sugar; beat until stiff. Fold egg whites into the chocolate mixture.
Carefully pour batter into prepared cake pan. Bake until cake is set and top is dull, about 20 minutes. Remove from oven and let cool on a wire rack.
Spray a 12-cup bowl with a 9-inch diameter with cooking spray; line with plastic wrap. Pack base of bowl and up the sides with chocolate ice cream; cover with plastic and press with your hands to make an even, smooth layer. Transfer to freezer and freeze until firm, about 2 hours.
Remove plastic wrap and form a layer of vanilla ice cream on top of the chocolate; cover with plastic wrap and press with your hands to make an even, smooth layer. Transfer to freezer and freeze until firm, about 2 hours.
Remove plastic wrap and form a layer of coffee ice cream on top of vanilla, leaving a small well in the center of the coffee layer; add sprinkles to well and cover with plastic wrap. Transfer to freezer and freeze until firm, at least 2 hours and up to overnight.
Place cake on a parchment-paper-lined baking sheet. Remove ice cream from freezer and remove plastic wrap; invert bowl over cake. Keep ice cream covered with plastic wrap, and return ice cream cake to freezer.
Preheat oven to 500 degrees (if not using a kitchen torch). Fill a pastry bag, fitted with a large star tip (such as Ateco No. 827), with meringue; pipe onto ice cream in a decorative fashion, or spoon meringue over ice cream and swirl with a rubber spatula. If ice cream starts to soften, return cake to freezer for 15 minutes.
Using a kitchen torch, heat meringue until it just starts to brown. Alternatively, place in oven and bake until meringue just starts to brown, 1 to 2 minutes. Remove from oven, transfer to a serving platter, and serve immediately.