FOR THE SHEET CAKE (Makes one 18-by-11-inch cake): Adjust oven rack to center position and heat oven to 350 degrees. Lightly grease 18-by-11-inch jelly roll pan. Line pan bottom and sides with waxed paper, allowing 1-inch overhang on each end. Do not grease paper.
Place egg whites in bowl of electric mixer; bring to warm room temperature over pan of hot water. Remove whites from pan of hot water and whip whites at medium speed until foamy. Add cream of tartar and salt, increase mixer speed to medium-high, and beat whites to soft but definite peaks. Slowly sprinkle on 3 tablespoons sugar; continue to beat until whites are shiny and very thick, 3 to 4 minutes. Scrape whites into wide 4-quart mixing bowl; set aside.
Without washing bowl or whisk attachment, add yolks to bowl; bring to warm room temperature over pan of hot water. Add vanilla and hot water; beat at high speed 1 minute. Slowly add remaining 1/2 cup sugar; beat until mixture is pale, shiny, and almost as thick as marshmallow cream, 4 to 5 minutes longer.
Scrape yolk mixture over egg whites; gently fold with rubber spatula until about two-thirds mixed. Sift flour over egg mixture; gently fold until flour is completely incorporated. Spread batter in prepared pan, running it up to edges and smoothing top with rubber spatula. Bake until cake top is lightly browned and center springs back when gently pressed, 12 to 15 minutes.
Immediately after baking, free the cake edges from the pan sides with a knife and smooth a sheet of waxed paper over the cake top. Place another sheet pan or cookie sheet on top of the cake. Flip over as shown, then lift off the baking pan. Let the cake cool completely, then gently peel the waxed paper off the cake bottom, removing the bottom crust. Flip the cake top side up, then peel off the second sheet of waxed paper, removing the top crust. (Can be wrapped in plastic, then in foil and refrigerate for 1 day). See illustrations 1-3 below.
FOR THE ALMOND COOKIES (Makes 36 marble-size cookies): Adjust oven rack to center position and heat oven to 350 degrees. Grease, then flour cookie sheet; tap off excess flour.
Finely grind almonds in food processor fitted with metal blade, about 1 minute. Add sugar; grind 15 seconds longer. Add egg and extract; process until mixture forms stiff dough that clumps around blade, 15 to 20 seconds longer.
Pinch off thirty-six raspberry-size pieces of dough, then roll each into smooth ball. Arrange balls 1/2-inch apart on prepared sheet. Bake until very lightly browned, 12 to 15 minutes. Let cool completely on sheet, then scrape free with metal spatula. (Can be stored in tightly covered container 1 week.)
FOR THE RASPBERRY PUREE (Makes 1 cup): Puree berries and sugar in blender or food processor fitted with metal blade. Strain through fine sieve, pressing on solids to release juice; discard seeds. (Can be covered and refrigerated 1 day.)
FOR THE RICH BAKED CUSTARD (Makes one 13-by-9-inch dish): Adjust oven rack to center position and heat oven to 300 degrees. Line pan bottom of large deep roasting pan with kitchen towel. Set Pyrex baking dish in roasting pan. Bring large kettle of water to boil.
Whisk yolks, sugar, and nutmeg in large mixing bowl. Meanwhile, bring milk and cream to gentle simmer in large saucepan, stirring frequently to prevent boiling over. Slowly whisk milk mixture into yolks; stir in brandy or Cognac. Set roasting pan in oven; pour custard into baking dish. Pour enough boiling water into roasting pan to reach mixture’s height. Cover roasting pan with heavy-duty foil.
Bake custard until spoonful taken from center is texture of soft yogurt, 45 to 55 minutes. Remove custard from oven; let cool to tepid in water bath. Remove dish from water bath, cover with plastic wrap, and refrigerate custard until completely cold. (Can be refrigerated overnight.)
FOR THE LEMON WHIPPED CREAM (Makes about 1 quart): Remove lemon zest with vegetable peeler. Squeeze, then strain enough juice from lemons to make 1/2 cup.
Finely grind zest with sugar in food processor fitted with metal blade, about 2 minutes. With machine running, gradually dribble in lemon juice. Scrape mixture into large airtight container. Stir in cream and sherry; cover tightly and refrigerate until mixture is thick and lemon-flavored, at least 12 hours. (Can be refrigerated up to 36 hours.)
Strain topping through fine-mesh sieve into bowl of electric mixer, pressing on zest to release cream. Whip cream to stiff peaks on medium-high.
FOR ASSEMBLING THE TRIFLE (See illlustrations 4 to 10 below): Brush the sheet cake evenly with cream sherry; let stand 10 minutes. Using a serrated knife, cut the cake into six lengthwise and eight crosswise strips to yield 48 approximate 2-inch squares.
Arrange 16 cake squares, shingling the squares around the bottom of trifle dish, placing 12 to 13 in a ring against the dish wall and the remaining squares in the center. Tuck 2 to 3 raspberries between the outer cake squares, using about 1/3 cup berries total. Scatter about 2/3 cup raspberreis over the top of the inner cake squares.
Dip 12 almond cookies into amaretto liqueur for 1 second, then place them on top of the outer cake squares. Drizzle 1/3 cup raspberry puree over the cake and cookies. Finally spread 1/3 of the custard over the layer, coming within 1/2-inch of the edge. Repeat cake/berries/cookie/puree/custard layering twice more to make a total of three layers. Cover the bowl with plastic wrap and refrigerate for at least 12, but no more than 36 hours.
No more than 8 hours before serving, fill a large pastry bag fitted with a 3/4-inch fluted tip with lemon whipped cream. Pipe large 2- to 3-inch high risettes over the trifle top. Pipe any remaining cream into tiny rosettes to fill in between the larger rosettes. Garnish the trifle with additional berries. Serve.