Prepare two 9-inch cake pans by lightly greasing them, lining them with waxed paper or parchment, greasing the paper, and lightly dusting with flour. Preheat the oven to 375 degrees F. and put a pan of water in the bottom of the oven. Mix the ground nuts together. Very finely chop the apples with a knife. You should have 1 3/4 cups. In a warmed electric mixer bowl, beat the eggs and egg yolk on high speed until doubled in volume. It may take 10 minutes or more. Slowly add the sugar while beating and continue beating until the volume is tripled. The eggs should be very thick and light in color. Don't be afraid of over-beating. Sift the flour over the egg mixture. Sprinkle the ground nuts over all, followed by the apples. With a large spatula, fold the mixture together rapidly but gently, being certain to bring all the elements from the bottom of the bowl up into the mixture. Divide the batter between 2 cake pans and bake in the middle of the oven for about 25 to 30 minutes, or until the top is golden brown and the sides have begun to pull away. Do not push on the meringue like top, or it may cave in. Place on a rack in a draft-free place and let cool completely. Lightly toast the pecan halves while the cake are in the oven. While the pecans are hot, quickly dip them in water and then roll them in granulated sugar until they are lightly coated. Let them dry on a rack. The cakes must be perfectly cool, or the heat with melt the cream. Invert the pans to remove the cakes, discarding the paper liners, and turn the cakes back over again so that the crusty top surface is in its original position. Place each cake on a serving platter. Using an electric standing mixer, fitted with a whip attachment, whip the cream with some sugar until stiff and place 8 dollops of the cream evenly around each cake. Garnish each bit of cream with a sugared pecan and serve with a shot glass of bourbon neat.