Preheat oven to 350 F.Butter the bottom and side of an 8-inch springform pan. Line the bottom with parchment paper. Wrap the outside with aluminum foil, extending all the way up the side.
In a small bowl, sift together the flour, baking powder, and salt.
In the bowl of a stand mixer or electric mixer using the whip attachment, beat the egg yolks on high for three minutes. Slowly add in 1 tbsp of sugar and continue beating until thick, light yellow ribbons form in the bowl, about 5 minutes. Beat in the vanilla extract.
Sift the flour mixture over the batter and fold in by hand.Fold in the melted butter.
Pour the mixture into a separate bowl and clean and dry your stand mixer bowl and beaters. Beat the egg whites and cream of tartar on high until frothy. Gradually add in the 1/4 cup of sugar and continue beating until stiff peaks form.
Fold 1/3 of the egg whites into the batter, then fold in the rest until well incorporated.
Gently spread the batter over the bottom of the prepared pan and bake until just set and golden, about 10 minutes. Don't let the top brown. To test cake for doneness, touch the cake gently in the center. If it springs, back, it's ready!
Place the cake on a wire rack to cool. Leave the oven on while you prepare the cheesecake batter.