Preheat oven to 350 ˚ F (180˚ C) and generously butter a 9-10” spring-form pan. Sift the cake flour, baking powder, and salt together in a medium-sized bowl and set aside.
Beat the egg yolks together in a large bowl with an electric mixer on high speed for 3 minutes. Then, with the mixer still running, gradually add the 1/3 cup of sugar and continue beating until thick light-yellow ribbons form in the bowl, about 5 minutes more. Beat in the vanilla and lemon extracts.
Sift the flour mixture over the batter and stir in by hand until no more white flecks appear. Then blend in the butter.
In a clean bowl, using clean dry beaters, beat the egg whites and cream of tartar together on high speed until frothy. Gradually add the remaining 2 Tbsp sugar and continue beating until stiff peaks form (the whites should stand up in stiff peaks but not be dry). Stir about 1/3 cup of the whites into the batter, then gently fold in the remaining whites- don’t worry if a few white specks remain.
Gently spoon the batter into the pan. Bake the cake just until the centre of the cake springs back when lightly touched, only about 10 minutes (watch carefully). Let the cake cool in the pan on a wire rack while you continue making the cheesecake filling. Do not remove the cake from the pan.
For Cream Cheese Filling:
Preheat oven to 350 ˚ F. (180˚ C) and generously butter a 9-10” spring-form pan. Make the batter for the sponge cake as the recipe directs. Evenly spread the batter on the bottom of the pan and bake just until set and golden, about 10 minutes. Place the cake on a wire rack to cool (don’t remove it from the pan).
While the cake cools, make the cream cheese filling:
Place one 8 oz. package of the cream cheese, 1/3 cup of the sugar, and the cornstarch in a large bowl. Beat with an electric mixer on low speed until creamy, about 3 minutes. Then beat in the remaining 3 packages of cream cheese. (I cut the bricks into 1” cubes).
Increase the mixer speed to high and beat in the remaining 1 1/3 cups of the sugar, and then beat in the vanilla. Blend in the eggs, one at a time, beating the batter well after adding each one. Blend in the heavy cream. At this point mix the filling only until completely blended. Be careful not to over-mix the batter.
Gently spoon the cheese filling on top of the baked sponge cake layer. Place the spring-form pan in a large shallow pan containing hot water that comes about 1 inch up the sides of the pan. Bake the cheesecake until the centre barely jiggles when you shake the pan, about 1 hour.
Cool the cake on a wire rack for 1 hour. Then cover the cake with plastic wrap and refrigerate until it’s completely cold, at least 4 hours, or overnight. Remove the sides of the spring-form pan. Slide the cake off the bottom of the pan onto a serving plate. Or if you wish, simply leave the cake on the removable bottom of the pan and place it on a serving plate. If any cake is left over, cover it with plastic wrap and store in the refrigerator.