Place a 10″ cast-iron skillet on the middle rack of the oven, and preheat to 450 degrees.
In a large bowl, whisk eggs together vigorously until light and frothy, about 2 minutes. Add milk, sugar, salt and vanilla, and whisk until combined. Sift in flour, and whisk just until smooth. Let rest for 5 – 10 minutes.
Carefully remove the skillet from the oven, add the butter and let melt completely, swirling the pan to allow the butter to coat the entire bottom. Pour batter into hot pan, and place back in the oven, shutting door quickly so oven loses as little heat as possible.
Bake for 15 minutes, until the sides have puffed up a lot, and the entire top of the pancake is golden brown. Remove from oven and use a spatula to loosen the edges of the pancake. Transfer to a serving platter, dust with powdered sugar and cut into large wedges. Serve immediately.