Heat the oil and butter in a 9 or 10-inch cast iron skillet set over medium heat. When the foam subsides, sauté the apples for 4-5 minutes, until softened and starting to turn golden on the edges. Sprinkle with sugar and cinnamon and cook for another minute or two, until the apples are golden and coated with cinnamon-sugar.
Meanwhile, whisk together the eggs, flour, and milk; don’t worry about getting all the lumps out.
Pour the batter evenly over the apples in the skillet and put it in the oven. (If you don’t have an ovenproof skillet, pour the sautéed apples into a buttered pie plate and pour the batter over them.)
Bake for 15-20 minutes, until the pancake is puffed and golden.
Cut it into wedges and serve warm, sprinkled with icing sugar and drizzled with maple syrup, or topped with a dollop of whipped cream.