Put the butter in a large, ovenproof, nonstick saute pan and place in the oven.
Meanwhile, in a blender, combine the eggs, flour, warm milk, sugar, vanilla extract and pinch of salt, and blend on medium-high speed until uniform. (If mixing by hand, combine the eggs with the milk until the mixture is light yellow and no longer stringy, about 1 minute. Add the flour, sugar, vanilla, and pinch of salt, and whisk vigorously to remove the lumps, about 30 seconds.)
Carefully remove the hot pan from the oven. The butter should be melted. Swirl the butter around the pan to coat completely, and then pour the remaining butter into the batter and pulse to blend. Pour the batter into the hot pan and return the pan to the oven. Cook until the pancake is puffed in the center and golden brown along the edges, 20 to 25 minutes.
Using a spatula, remove the entire Dutch baby from the pan and place on a cooling rack for a few minutes to allow the steam to escape without condensing along the bottom and rendering the pancake soggy. Dust with confectioners' sugar when cooled slightly. Slice the pancake into 8 wedges on a serving platter or cutting board.