For the Sponge Cake:
Preheat oven to 325 degrees F. Grease and lay parchment paper over the bottom of a jelly roll size baking pan (17 1/2 inches by 11 1/2 inches by 1-inch deep). With an electric beater, beat together the egg yolks, just 1/4 cup of the sugar (reserving the rest), and vanilla until the mixture becomes a pale yellow and thickens. Sift cake flour over the egg yolk mixture and set aside briefly. Wash and dry the beaters.
In a separate metal bowl, beat the egg whites and cream of tartar together and gradually beat in the balance of the sugar until stiff peaks form. To the egg yolk/flour bowl, fold in 1/3 of the beaten egg whites until just barely combined. Repeat two more times with each of the remaining 2/3 of the beaten egg whites.
Spread into jelly roll pan and bake in oven for about 15 minutes or until the surface is golden brown and springs back when touched. Let cake cool in pan for 10 minutes and loosen the edges with a spatula or butter knife. Then, invert cake onto a similarly sized baking sheet without edges, by holding against the top edges of the jelly roll pan and flipping it over. Peel off parchment paper and let cool completely. Wash the jelly roll pan, to have ready for soaking the cake.
For the Strawberries and Whipped Topping:
Reserve 18 whole (but cleaned) berries. To begin the maceration process, slice the rest of the berries into a bowl, mix in the sugar, and refrigerate.
Whip the heavy cream with an electric beater until stiff peaks form.
Cook's Note: Each individual serving will have two layers of cake. You can adjust the serving size based on the way you slice the cake. If serving in martini glasses (as was done on the episode), cut the cake into rectangles which are approximately 3 inches square (a count of 4 across the width of the sheet cake and 6 along the length of the cake). This will yield 24 rectangles for 12 servings. You can also make slightly larger servings if using a flat serving plate by cutting into 12 rectangles which are about 4 inches square. Return the cake squares to the jelly roll pan and pour the cold tea over them allowing to soak.
Use a spatula to transfer a slice of cake to each of the serving glasses or plates. Spoon some of the macerated strawberries on top of each cake round and top with vanilla cream. Cover with the second layer of sponge cake, then more strawberries, then more vanilla cream, and top with a dollop of whipped cream around which you will arrange 3 whole strawberries and a sprig of fresh mint.