Preheat the oven to 450°.
Peel and core the apples. Coarsely chop 2-1/2 of the apples. Slice the remaining 1/2 apple into thin spirals for garnish on top. Brush the spirals with lemon juice to prevent them from darkening, and set them aside.
Mix the eggs, flour, baking powder, salt, sugar, milk, vanilla, cinnamon, and the chopped apples together in a bowl. Beat until they are combined, although the batter will remain lumpy.
Melt the butter in a 10-in cast iron frying pan. Pour the batter into the pan, and arrange the reserved apple spirals on top.
Bake the pancake in the oven at 450° for 15 minutes. Then turn the oven down to 350° and continue to bake the pancake an additional 40 minutes, or until a toothpick inserted in the center comes out clean. Remove the pan from the oven and allow it to rest for 5 minutes.
Sprinkle the brown sugar over the top of the pancake, cut into wedges, and serve with the warm maple syrup.