Preheat the oven to 425 degrees F.
Blend the eggs, flour, milk, sugar, and cinnamon until combined and there are no lumps.
Place the butter in a heavy bottomed, oven-safe, 9" skillet, and put both of those in the hot oven. WATCH through the oven door until the butter melts.
As soon as the butter melts, remove the skillet from the oven and pour the batter into it. Place it back in the oven and bake for 20 minutes. After 20 minutes, turn the oven off, but leave the Dutch baby in the oven for another 5 minutes.