Brush the butter and flour mixture over the inside of 2 pie pans, 10 inches (25 cm) in diameter (or use pan spray). Reserve.
Stir together the egg whites and one-third of the half-and-half. Reserve.
Sift together the cake flour, granulated sugar, baking powder, and salt. Add the vanilla, melted butter, the remaining half-and-half, and the whole egg. B