To skin the hazelnuts, toast them and put them on an old, clean towel. Fold it and rub them against each other vigorously.

FOR THE MERINGUE: Adjust oven rack to middle position and heat oven to 250 degrees. Using ruler and permanent marker, draw 13 by 10½-inch rectangle on piece of parchment paper. Grease baking sheet and place parchment on it, ink side down. Grease parchment paper.

Process almonds, hazelnuts, cornstarch, and salt together in food processor until nuts are finely ground, 15 to 20 seconds. Add ½ cup sugar and pulse to combine, 1 to 2 pulses.

Using stand mixer fitted with whisk, whip egg whites and cream of tartar together on medium-low speed until foamy, about 1 minute. Increase speed to medium-high and whip whites to soft, billowy mounds, about 1 minute. With mixer running at medium-high speed, slowly add remaining ½ cup sugar and continue to whip until glossy, stiff peaks form, 2 to 3 minutes.

Fold nut mixture into egg whites in 2 batches. With offset spatula, spread meringue evenly into 13 by 10½-inch rectangle on parchment, using lines on parchment as guide. Using spray bottle, evenly mist surface of meringue with water until glistening.

FOR THE BUTTERCREAM: Heat milk in small saucepan over medium heat until just simmering. Meanwhile, whisk egg yolks, sugar, cornstarch, and salt together in bowl until smooth. Remove milk from heat and, whisking constantly, add half of milk to yolk mixture to temper.

Whisking constantly, return tempered yolk mixture to milk in saucepan. Return saucepan to medium heat and cook, whisking constantly, until mixture is bubbling and thickens to consistency of warm pudding, 3 to 5 minutes. Transfer pastry cream to bowl. Cover and refrigerate until set, at least 2 hours or up to 24 hours. Before using, warm gently to room temperature in microwave at 50 percent power, stirring every 10 seconds.

Stir together amaretto and espresso powder; set aside. Using stand mixer fitted with paddle, beat butter at medium speed until smooth and light, 3 to 4 minutes. Add pastry cream in 3 batches, beating for 30 seconds after each addition. Add amaretto mixture and continue to beat until light and fluffy, about 5 minutes longer, scraping down bowl thoroughly halfway though mixing.

FOR THE GANACHE: Place chocolate in heatproof bowl. Bring cream and corn syrup to simmer in small saucepan over medium heat. Pour cream mixture over chocolate and let stand for 1 minute. Stir mixture until smooth. Set aside to cool until chocolate mounds slightly when dripped from spoon.

Place 3 rectangles on wire rack set in rimmed baking sheet. Using offset spatula, spread ¼ cup ganache evenly over surface of each meringue. Refrigerate until ganache is firm, about 15 minutes. Set aside remaining ganache.

Using offset spatula, spread top surface of remaining meringue rectangle with ½ cup buttercream; place on wire rack with ganache-coated meringues. Invert one ganache-coated meringue, place on top of buttercream, and press gently to level. Repeat 2 more times, spreading meringue with ½ cup buttercream and topping with inverted ganache-coated meringue.

When last ganache-coated meringue is in place, spread half of remaining buttercream to lightly coat sides of cake, then use remaining buttercream to coat top of cake. Smooth sides and top until cake resembles box. Refrigerate until buttercream is firm, about 2 hours. (Once buttercream is firm, assembled cake may be wrapped tightly in plastic wrap and refrigerated for up to 2 days.)

Garnish top of cake with toasted whole hazelnuts. Holding cake with 1 hand, gently press sliced almonds onto sides with other hand. Chill for at least 3 hours or up to 12 hours.

Transfer to platter. Cut into slices and serve. For best results, slice with sharp knife that has been dipped in hot water and wiped dry before each slice.