Combine 1 1/2 cups sugar and 1/4 cup water in heavy small saucepan. Stir over medium heat until sugar dissolves. Increase heat and boil without stirring until color is deep amber, occasionally swirling pan and brushing down sides with pastry brush dipped into water, about 8 minutes. Working quickly, divide hot caramel among six 1 1/4-cup custard cups. Using pot holders to protect hands, tilt and rotate custard cups to cover bottoms with caramel. Set aside.
Melt 2 tablespoons butter in large nonstick skillet over medium heat. Add apple wedges and sauté until just tender, about 12 minutes. Arrange apple wedges in bottoms of caramel-lined custard cups.
Preheat oven to 325°F Sift cake flour, baking powder, and salt into medium bowl. Using electric mixer, beat remaining 1/2 cup butter and remaining 3/4 cup sugar in another medium bowl until well blended. Add eggs 1 at a time and beat until well blended after each addition. Mix in vanilla extract. Beat in flour mixture in 3 additions alternately with whole milk in 2 additions. Spoon batter over apples in custard cups, dividing batter equally (about 1/2 cup for each).
Bake cakes until light golden around edges and tester inserted into center comes out clean, about 35 minutes. Run small knife around cakes to loosen. Invert cakes onto plates. Serve warm with vanilla ice cream.