Blend the batter: Place the flour, milk, eggs, sugar, vanilla, and salt in a blender or food processor fitted with the blade attachment. Blend for 10 seconds, scrape down the sides, and then blend for another 10 seconds. The batter will be quite loose and liquidy.
Rest the batter: Leave the batter in the blender and set aside to rest 20 to 25 minutes. This gives the flour time to absorb the liquid.
Heat the pan and oven: Meanwhile, place the skillet you’re using on a middle rack to warm along with the oven. Heat the oven to 425°F.
Melt the butter: When ready to make the pancake, remove the skillet from the oven using oven mitts and place it on top of the stove. Add the butter and swirl the pan to melt the butter and coat the bottom and sides of the pan.
Add the batter: Pour the batter on top of the butter. Tilt the pan if needed so that the batter runs evenly to all sides. Place the skillet in the oven.
Bake the Dutch baby: Bake until the Dutch baby is puffed, lightly browned across the top, and darker brown on the sides and edges, 15 to 20 minutes.
Serve while hot: You can either serve from the pan or transfer the Dutch baby to a serving platter. Dust with powdered sugar. Cut into wedges and serve
Fruit-filled Dutch baby: Arrange fruits like blueberries, raspberries, or sliced peaches over the bottom of the skillet and then pour the batter over top. (Scattering fruit on top of the batter will keep it from rising as impressively.)