Place one tablespoon butter in a 9-12 inch cast iron skillet or 9 inch pie plate. Place in the oven for 5 minutes.
Combine the sugar and cinnamon in a small bowl.
Put the flour, milk, eggs, vanilla, and remaining cold butter in a blender. Blend until well blended. Scarp down the sides and blend for about 30 seconds more.
Remove the skillet or pan from the oven and swirl the butter all around. Sprinkle with 1/3 of the cinnamon sugar and then pour the batter into the skillet. Place in the oven at 450 degrees for 20 minutes. DO NOT OPEN the oven during this first 20 minutes! After 20 minutes turn the oven down to 350 degrees and bake for another 15-20 minutes until the edges begin to brown.
Remove from oven and let cool for 3-5 minutes. Brush or drizzle with the remaining melted butter, then cover in more cinnamon sugar. Serve immediately.
* It is extremely important not to open the oven until the last 5-10 minutes of baking. If you let the steam out, the dutch baby will not puff properly.