Place the eggs and milk in the blender. Cover and pulse a couple times. Allow the egg mixture to sit and warm to room temperature while you preheat the oven. (Room temperature eggs and milk equal fluffy Dutch babies.) Preheat the oven to 425 degrees F. Remove the upper rack and place two large 11- to 14-inch cast iron skillets in the oven to preheat.
Once the oven and skillets are piping hot, add 2 tablespoons of butter to each skillet and close the oven door. Melt the remaining butter. Add the flour, sugar, salt, and vanilla to the blender. Puree until smooth and bubbly. Then pour in the melted butter and puree again.
Open the oven door and use an oven mitt to swirl the skillets to coat the bottom with the melted butter. Then pour equal amounts of batter into each skillet and quickly close the oven door. Lower the temperature to 375 degrees F. Bake the Dutch babies for 25-35 minutes until puffy and golden.
Use an oven mitt and spatula to move the Dutch babies out of the skillets and onto a cutting board. They will deflate quickly. Sprinkle with sugar and cut into wedges. Serve each Dutch baby with a squeeze of lemon juice, or other optional toppings.
OPTIONAL TOPPINGS: Sugar and lemon wedges, fresh berries, ground coffee and sweetened condensed milk, jam, honey and peaches.