For the 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 by 11 1/2 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, gradually beating in the balance of the sugar until stiff peaks form. To the egg yolk/flour bowl, fold in one-third of the beaten egg whites until just barely combined. Repeat two more times with each of the remaining two thirds of the beaten egg whites. Spread into baking 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.
While the cake is cooling, it would be a good idea to make room in the freezer for the sheet cake.
When the cake is completely cool, peel off the browned surface of the cake. (You can do this simply by loosening it and rolling it off.)
Then prepare the ice cream by cutting each 1/2 gallon crosswise into 7 even-sized bricks, a total of 14 bricks. The typical rectangular carton of ice cream measures 63/4 inches long by 5 inches wide by 3 inches tall. You will arrange these bricks 4 across and 3 lengthwise on top of the sheet cake, cutting the leftover bricks to size to fit in any areas of the cake that are not covered by the ice cream. You will need to work quickly to keep the ice cream from melting. (If the ice cream is allowed to melt, its texture will not be optimal when the cake is frozen.) Cut the ice cream covered 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 of 2 petit fours each. As you cut, you will need to remove 1 row and 1 length of the cake squares to another platter. Then use the knife to gently separate all the ice cream covered the squares, allowing enough space between them so that you will be able to thoroughly coat each piece with chocolate.
Put all the ice cream covered cake into the space you have reserved in the freezer. Let freeze for about an hour.
The chocolate to coat the cake and ice cream will be tempered, a term used to describe the successive melting and cooling of the chocolate within a certain temperature range. This process allows the molecules of the chocolate to align so that it will retain a silky appearance without a chalky finish. To temper the chocolate, place half of the semisweet chocolate pieces in each of 2 stainless steel bowls which will fit over a saucepan double-boiler fashion. Bring an inch or so of water to a boil in the saucepan and fit 1 of the bowls of chocolate pieces over it and heat until just melted (no more than 120 degrees F on the candy thermometer). Then pour this just-melted chocolate into the other bowl with the un-melted chocolate, melt and stir to combine until chocolate reaches between 86 and 90 degrees F. Remove the tray of ice cream covered cake from the freezer and work quickly to spoon the chocolate over the ice cream and cake before the chocolate hardens. Completely coat each piece with chocolate and return to freezer. Return to freezer and remove from tray with a thin bladed spatula to serve.
Recipe courtesy of Robert Irvine with Brian O'Reilly, Harper Collins Publishers, copyright 2007.