You must have a non-stick skillet or this won't work. Whisk sugar, flour, baking powder and 1/4 teaspoon salt together. Beat milk with eggs and vanilla and whisk this into batter; let stand while you cook the apples.
Melt the butter in a large skillet. When foaming subsides, add the apples, cover and cook gently for 5 minutes or until soft. Uncover, raise the heat and evaporate the moisture. When the moisture has almost completely evaporated, add the sugar and finish boiling the juices away.
Preheat the broiler with rack set 6 to 7 inches away from heat source.
Oil the bottom and sides of a 10-inch non-stick pan with butter or non-stick vegetable cooking spray and heat for a minute. Add 1/3 cup of batter to the pan and tilt so it is well coated. Set skillet on very low heat and cook for 30 seconds. Gently arrange about 1/4 of the apple mixture on the first pancake. Pour in 1/3 cup more batter over the apples to cover them as best as possible. Cook pancake for a minute over medium heat, lower the heat and cook 2 minutes longer. Broil for about 3 minutes or until pancake is cooked through and golden. With a spatula loosen pancake around the edges and transfer to a platter (cover loosely with foil until all 4 pancakes are done or serve immediately). Repeat procedure with other 3 pancakes; serve dusted with confectioner's sugar.