Have two glass pie plates ready to go when the oven is preheated - put 2 Tbsp of butter in each.
Prep the batter: In a blender, combine the eggs, flour, milk, salt, vanilla and sugar, mixing well and using a spatula to scrape as needed.
When the oven is ready, put the pie plates in for 5 minutes, to heat them and melt the butter. After 5 minutes, remove the plates from the oven, and swirl the to coat evenly with the melted butter. Carefully pour 1/2 of the batter into each plate, and return to the oven to bake for 25 minutes. Do not peek at them or open the door during this time.
While that cooks, make the lemon sugar - zest the two lemons, and stir the sugar to combine.
When done, remove the dutch babies from the oven - they will be puffed and glorious! Serve immediately, and top with the lemon sugar.
Notes
My mom (Nana, to her grandkids) is famous for these at our house in Maine. Thanks Nana!