Preheat the oven to 350 F and generously butter a 9-inch springform pan.
I would wrap outside of pan with foil as mine leaked a bit!
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 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.
Sift the flour mixture over the batter and stir it in by hand until mo 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 until frothy.
Gradually add the remaining 2 tablespoons 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.
Gently spoon the batter into the pan.
Bake until just set about 13-15 minutes.
Cool in the pan on a wire rack while you make the cheesecake filling which will go right on top of this.