Preheat your oven to 425 degrees.
As the oven heats, prepare a 9-by-13-inch baking dish by placing the butter in the center of the baking dish. Place the dish in the oven and allow the butter to melt for about 5 minutes.
Meanwhile, crack the eggs into in a large bowl and beat them with a whisk until they are light in color and frothy. Add the milk, flour, pure vanilla extract, and salt and whisk until the batter is well blended.
Remove the baking dish from the oven and pour the batter over the melted butter. Bake the pancake for 22-25 minutes or until it is golden brown and has puffed up on the sides.
Sprinkle the pancake with powdered sugar and top with your choice of fresh fruit and syrup. Serve immediately.
A Dutch baby pancake will deflate slightly after being removed from the oven and allowed to sit at room temperature.