Preheat broiler.

For the batter: in a blender or food processor, combine the eggs, vanilla, and 3/4 cup sugar. Blend for about 15 seconds, until combined. Add the flour and baking powder and mix for 60 seconds more, or until very smooth. Set the batter aside.

Heat a 12-inch nonstick skillet over medium heat and melt the butter. Add the apples and cook until softened, about 4 to 5 minutes. Add the cinnamon and remaining 1 1/2 tablespoons sugar, sprinkling them evenly over the apples, and cook, stirring, until the apples are glazed and slightly translucent at the edges, about 2 minutes.

Distribute the apples evenly in the skillet and pour the batter over them. (Chef's Note: You may also make 4 individual pancakes, using a smaller pan. Just use 1/4 of the apples and 1/4 of the batter for each.) Cook until the bottom seems quite firm, about 8 minutes. Transfer the pan to the broiler and, while watching carefully, cook until the pancake is firm throughout and golden on top.

Cut the pancake into 4 wedges and transfer them, apple side up, to serving plates. Sprinkle with the confectioners' sugar, place a dollop of crème fraiche on top, and garnish with the strawberries.