Prepare a mound of wood coals (see How to build a great campfire for cooking), hardwood lump charcoal, or charcoal briquettes.
Meanwhile, whisk together the eggs, milk, and flour mixture in a medium bowl until well blended.
Move about a quart’s worth of coals to the cooking pit and arrange them in a ring. Lightly spray a dutch oven with oil and heat it over the coals. Melt the butter in the oven, then pour in the egg mixture. Spread the apples evenly over the surface and sprinkle with the remaining ¼ cup (103 g) sugar and the remaining ¼ teaspoon cinnamon. Cover and place 1½ rings of coals on the lid.
Bake over medium heat for 20 to 25 minutes, or until the pancake is puffed and golden all over. (Call the kids over to ooh and ahh at your creation once you take the oven off the heat, because the pancake will deflate shortly after the lid is removed.)
Dust the pancake with powdered sugar before serving.