Heat the oven to 400°F (200°C). Put the butter in a 6.5-inch cast iron skillet or 5×5-inch baking dish and place it in the oven so the butter melts and the pan heats.
In a small bowl, whisk the egg, milk, vanilla, and sugar until combined. Add the flour and salt and whisk until the batter is smooth with no lumps.
Carefully remove the hot pan from the oven. Swirl the melted butter to coat the bottom and sides, then scatter the blueberries evenly over the bottom.
Pour the batter over the blueberries. Bake for 20 to 25 minutes, until the edges are puffed and deep golden and the center is set.
Lift the Dutch baby out with a spatula onto a plate. Dust with confectioners' sugar, add a few more berries if you like, and serve right away before it deflates.
Notes
Get the pan hot first. Preheat the skillet or baking dish with the butter in it so the batter hits a hot, buttered surface. That heat is what makes the Dutch baby climb the sides and puff.Use a small pan. A 6.5-inch cast iron skillet or 5×5-inch oven-safe baking dish gives the tallest rise. A bigger pan spreads the batter thin, and you'll end up with a flatter pancake.Whisk the batter smooth. Beat out the flour lumps so the batter is thin and pourable, close to the consistency of cream. Lumps bake into dense spots.Choose fresh blueberries when you can. They give the highest rise. Frozen berries are colder and wetter, which can hold the puff back a little.Watch for puffed, golden edges. The Dutch baby is done when the edges are tall and deep golden and the center is set, usually 20 to 25 minutes. If the middle still looks wet, give it a few more minutes.Serve it right away. Dutch babies deflate as they cool, so have your confectioners' sugar and any toppings ready before it leaves the oven.If doubling the recipe use a 10-inch cast iron skillet.