Preheat your oven to 450F. Place the skillet in the oven to heat it up while the oven warms. Melt 2.5 tbsp of butter in the microwave. In a blender, pulse three eggs. Add flour, milk, sugar, salt, and vanilla, and 2 tbsp of the melted butter. Blend until well-combined. Drizzle the remaining half tablespoon of the melted butter into the hot skillet until the surface is greased. Pour the batter into the hot, buttered skillet. Bake in the oven for 13-15 minutes, or until the dutch baby is puffy, and slightly golden brown on top. Don’t open the oven during cooking! Top with powdered sugar, syrup, or your other favorite pancake toppings.