In a blender, combine the eggs, milk, flour, sugar, vanilla extract, and salt. Blend until smooth and no lumps remain. Let batter rest for about 10 minutes while oven preheats.
Carefully take the hot skillet out of the oven. Add the butter to the skillet and swirl it to coat the bottom and sides. Scatter the blueberries over the melted butter.
Pour the batter over the blueberries in the skillet. Return the skillet to the oven and bake for 20 minutes, until the Dutch baby is puffed and golden brown.
Take the dish out of the oven. Dust it with confectioners' sugar if you like. Slice and serve right away.