For meringue layers:
Position rack in center of oven and preheat to 175°F. Using pencil, trace two 12 x 4-inch rectangles on sheet of parchment paper; turn parchment over (rectangles will show through) and place on large rimmed baking sheet. Trace one 12 x 4-inch rectangle on second sheet of parchment paper; turn parchment over and place on second rimmed baking sheet.

Sift powdered sugar, superfine sugar, and salt into medium bowl. Combine egg whites and cream of tartar in large bowl of heavy-duty stand mixer fitted with wire whisk; beat on medium-low speed until frothy. Increase speed to medium-high and beat until soft peaks form. Increase speed to high; gradually add sugar mixture and beat until stiff and glossy peaks form, about 3 minutes. Beat in vanilla and peppermint extracts. Divide meringue equally among prepared rectangles on parchment (about 1 1/3 cups for each); spread meringue evenly within traced lines.

Bake meringues until dry and crisp but not browned, about 3 hours. Turn off oven and let meringues cool completely in oven.

Carefully remove meringue rectangles from parchment. DO AHEAD: Meringues can be made 1 week ahead. Store in single layer in airtight container at room temperature.

For peppermint syrup:
Combine 1/2 cup water and sugar in small saucepan. Stir over medium heat until sugar dissolves and mixture comes to boil. Remove from heat; stir in peppermint schnapps. Transfer to bowl; cover and chill until cold. DO AHEAD: Can be made 3 days ahead. Keep chilled.

For cake:
Position rack in center of oven and preheat to 350°F. Lightly butter bottom and sides of 13 x 9 x 1-inch baking sheet. Line bottom of baking sheet with parchment paper. Lightly dust sheet sides with flour. Sift 1/2 cup flour, cocoa powder, baking powder, and salt into medium bowl. Using electric mixer, beat eggs and egg yolks in another medium bowl until pale and foamy, about 2 minutes. Add sugar and vanilla; beat until mixture is thick and ribbon forms when beaters are lifted, about 3 minutes. Sift flour mixture over egg mixture and gently fold in with rubber spatula just until incorporated.

Transfer batter to baking sheet; spread evenly to edges. Bake until top springs back when gently touched and tester inserted into center comes out clean, about 15 minutes. Transfer baking sheet to rack and cool cake 20 minutes. Run small knife around sides of cake to loosen. Invert cake onto parchment-lined work surface; gently peel off parchment. Cool completely. Using serrated knife, cut cake in half lengthwise, then trim each half to 12 x 4-inch rectangle.

For buttercream:
Simmer cream, butter, and corn syrup in medium saucepan.Remove from heat. Add chocolate; whisk until smooth. Whisk in vanilla and salt. Let stand at room temperature until thick enough to spread, 1 hour to 1 1/2 hours. DO AHEAD: Can be made 4 hours ahead. Let stand at room temperature.

Transfer 1/2 cup buttercream to pastry bag fitted with medium star tip; reserve for piping rosettes. Brush off any crumbs from meringue layers and cake layers. Place several small dabs of buttercream down center of 15-inch-long rectangular serving platter. Place 1 meringue layer, top side up, atop buttercream on platter, anchoring to platter. Place strips of foil around meringue layer to protect platter when spreading meringue with buttercream. Using small offset spatula, spread 2/3 cup buttercream over meringue. Top with 1 cake layer, top side down, pressing gently to adhere. Brush cake layer with 1/3 cup peppermint syrup (cake layer will be very moist). Spread 2/3 cup buttercream over, then top with second meringue layer, top side up. Spread 2/3 cup buttercream over. Cover with second cake layer, top side down. Brush with 1/3 cup peppermint syrup (cake layer will be very moist). Spread with 2/3 cup buttercream. Top with third meringue layer, top side up. Spread thin layer of buttercream over top and sides of cake. Chill 15 minutes.

Spread remaining buttercream over top and sides of cake. Pipe small rosettes of buttercream in 2 rows atop center of cake. Stand 1 or 2 mint wafer triangles in each rosette. Chill cake at least 6 hours. DO AHEAD: Can be made 2 days ahead. Cover loosely; chill. Let cake stand at room temperature 1 1/2 hours before serving.

Garnish top of cake with fresh raspberries and mint leaves and serve.