Place a rack in the middle of the oven and preheat to 415°F / 210°C.
Place a 10" cast iron pan in the oven to heat while making batter. (You could also use a heavy-bottomed frying pan or a pie plate.) Let the pan heat in the oven for at least 5 - 10 minutes. It needs to be hot.
Add milk, eggs, flour, sugar, salt, and lemon zest or vanilla, if using, to a blender. Blend until well combined and very smooth. Scrape down the sides of the blender jar, if necessary, to incorporate all of the flour. (You can also mix by hand, if preferred.)
Open the oven door and place the butter into the hot pan. When the butter has melted (watch it, so it doesn't burn), remove the skillet from the oven and carefully pour the batter into the hot pan. Immediately place the pan back into the oven.
Bake for 20 minutes, then lower the oven to 325°F / 160°C and bake for an additional 5 minutes, until puffy and deep golden brown. (Do not open the oven while baking!)
While Dutch baby is baking, make lemon glaze, if desired. Place butter, powdered sugar and lemon juice in a bowl and stir with a fork until well combined and smooth. Set aside until serving.
Remove from the oven, dust with powdered sugar, and cut into 4 wedges. Serve immediately, with berries, syrup or with lemon glaze. Pancake will deflate slightly after removing from the oven.