Preheat oven to 425F with the oven rack on the middle of your oven. Place an 8 or 10 inch heavy ovenproof frying pan or a cast iron skillet in the oven while it is preheating.
In a large bowl or blender, combine the eggs, milk, flour, vanilla extract, and sugar. Beat for 5 minutes until smooth and creamy.
When the oven is up to temperature, using pot holders, remove the hot skillet from the oven (or do this very carefully on the rack). Add the butter; tilting the pan to melt the butter and coat the skillet. Pour the prepared batter into the hot skillet, all at once, and immediately return the skillet to the oven.
Bake approximately 15-20 minutes or until puffed and golden brown, watching carefully. The pancake should puff up around the edges; it may puff irregularly in the center.
Carefully remove the pancake from the oven and serve immediately. For a classic German/Dutch Baby Pancake, dust the top with powdered sugar.
Notes
For a 12 inch frying pan (and more servings), you can double the ingredients.
I am not a health professional and nutrition data is calculated programatically. Accuracy may vary with product selection, calculator accuracy, etc. Consult a professional for the best information.