In a blender or a food processor, blend together eggs, milk, flour, sugar, vanilla, salt, and nutmeg.
Let the batter rest in the blender. Meanwhile, place butter in an oven-safe skillet and place in cold oven.
Preheat oven to 400ºF.
When preheated, carefully remove pan, swirl butter around to coat pan, and pour batter in.
Return to oven and cook for 20-25 minutes or until no longer jiggly in the center.
Dust with powdered sugar and serve immediately.
Notes
Dutch babies are best enjoyed fresh, but store leftovers in a covered container in the fridge for 2-3 days. Dutch babies are best stored with no toppings.
Reheat in the microwave for 20-30 seconds or until warmed through.