Heat the oven to 425°. Peel and quarter the apple, then trim away the core. Thinly slice the quarters.
In a small bowl, mix 2 tablespoons of the sugar and 1/4 teaspoon of the cinnamon with a fork. Add the apple slices and toss until they're well coated.
Slice the butter into two equal pieces and place them in a 9- or 10-inch glass pie pan or ovenproof skillet.* Put the pan in the oven until the butter melts, about 2 minutes, then use an oven mitt or hot handle holder to remove it from the oven, and swirl the pan to coat its surface.
Spread the apples over the bottom of the pan. Bake until the apples have softened slightly and the butter is bubbling and beginning to brown around the edges, about 10 minutes.
Meanwhile, make the pancake batter. In a blender, combine the eggs, milk, flour, salt, vanilla, and the remaining sugar and cinnamon. Blend the ingredients on medium speed until they're well mixed and frothy, about 1 minute.
Use an oven mitt to carefully remove the dish from the oven. Pour the batter over the apples, then bake the pancake until it's puffy and golden brown, about 25 to 30 minutes. Let it cool slightly on a wire rack. (Note: it will deflate quite a bit.) Dust the pancake with confectioners' sugar and cut into wedges before servering.
*It's best to use a pan at least 9 inches wide. In a smaller pan, the pancake will take longer to cook and be moister and more custardlike.