Nutrition per serving may change if servings are adjusted.
1/3 cup sweetened shredded coconut
1/3 cup sliced almonds
2/3 cup confectioners’ sugar, plus more for dusting
2 tablespoons cornstarch
5 large egg whites, at room temperature (see Tip)
1/4 teaspoon cream of tartar
3/4 cup granulated sugar
1 teaspoon vanilla extract
3 cups mango sorbet
Position racks in top third and middle of oven. Preheat to 350°F. Line 2 large baking sheets with parchment paper. Using a 9-inch springform pan as a guide, draw 3 circles on the parchment paper with a pencil. Turn the paper over (the lines will show through). (Alternatively, line baking sheets with foil, coat with cooking spray and dust with flour. Trace circles with your finger.)
Spread coconut and almonds in two pans and toast in the oven, about 5 minutes for the coconut and 8 minutes for the almonds. Let cool slightly. Transfer both to a food processor, add confectioners' sugar and cornstarch and process to a coarse powder. Reduce oven temperature to 250°F.
Beat egg whites and cream of tartar in a mixing bowl on low speed until frothy. Gradually increase the mixer speed to high and beat until soft peaks form. Decrease the speed to medium and slowly beat in granulated sugar. Add vanilla and beat until stiff peaks form. Sprinkle the almond/coconut mixture over the meringue and gently fold in with a rubber spatula.
Spoon one-third of the meringue into a pastry bag fitted with a 1/2-inch open-star or plain tip. Pipe the meringue in a tight spiral onto one of the circles on a prepared baking sheet—this will be the top layer. Spread the remaining meringue within the outlines of the other 2 circles, making sure the meringue is level and smooth.
Bake the meringue circles until golden and firm to the touch, 50 to 70 minutes, switching the positions of the sheets after 30 minutes of baking. Let cool completely on the baking sheets on wire racks. Carefully peel off the paper.
Let sorbet soften in the refrigerator for 30 minutes. Carefully trim the meringue layers with a sharp knife to fit snugly into the 9-inch springform pan. Set a plain meringue circle in the bottom of the pan and spread with half of the sorbet. Set the second plain meringue circle on top and cover with the remaining sorbet. Top with the decorative meringue circle. Cover with plastic wrap and freeze overnight.
Before serving, let the torte soften for 30 minutes in the refrigerator. Run a knife around the inside of the pan to loosen the torte. Remove the pan's outer ring. Dust the top with confectioners' sugar and transfer to a cake plate.
Tip: To bring an egg to room temperature: Either set it out on the counter for 15 minutes or submerge it (in the shell) in a bowl of lukewarm (not hot) water for 5 minutes.