Pre-heat oven to 425 F, place a 10" cast iron skillet in the oven so it heats up with the oven.
Prepare the batter: combine the eggs, milk, vanilla, sugar, salt, and flour in a mixing bowl or the bowl of a blender / food-processor. Mix well using a blender, food processor, or immersion blender. Alternatively, a hand whisk can be used (see notes below).
Allow the batter to rest while the oven comes to temperature, at least 10 minutes.
Remove the skillet from the oven, place the butter in the hot skillet and swirl in circles so that the melted butter coats the sides.
Give the batter one more whirl in the blender or food processor (or a couple of good whisks). Pour the batter into the hot skillet and place back in the oven. Cook for 15 minutes undisturbed.
Reduce the heat to 350 F and bake until the pancake is puffed up and golden. 5-10 minutes more.
Once cooked, remove from the oven and dust with powdered sugar, fresh fruit, or other deisred toppings. Enjoy while still hot and puffed up.