As soon as the apples are cooking, get started on the Dutch baby.
Position a rack in the center of the oven, and set your pie pan on the rack. Preheat the oven to 425 F with the pan inside.
In a bowl, whisk together the flour, sugar and spices. Separately, whisk together the milk, eggs, vanilla and orange zest. Slowly pour half the liquid into the flour mixture, whisking well to form a smooth paste. Gradually whisk in the remaining liquid until smooth, and whisk well for 15 seconds. Let the batter rest for 10 minutes while the oven preheats.
Once the batter has rested and the oven is preheated, open the door and drop the butter into the pan. Close the door again while the butter melts. When the butter is sizzling hot and just starting to brown a little, it's time to add the pancake batter.
Take the hot pan out of the oven, and use a pastry brush to brush the butter up the sides of the pan so that the bottom and sides are well coated in butter. Pour the batter right into the sizzling butter. Return the pan to the oven. Bake at 425 F for 15-18 minutes, until the edges are puffed up and golden brown. DO NOT open the oven door early to peek, or your Dutch baby might not puff up as well. After 15 minutes, turn the oven off, but let the Dutch baby sit in the oven for 5 more minutes.
Your pancake is ready to eat! The sides should have puffed and risen dramatically, forming a big pancake "bowl" that you can fill with the cinnamon apples or any fruit you like. Cut into portions and serve immediately.