Preheat your oven to 425°F (220°C). Place a 9x13-inch baking dish in the oven to heat up while you prepare the batter.
In a large mixing bowl, whisk together the eggs, milk, flour, salt, and vanilla extract until smooth and well combined.
Carefully remove the hot baking dish from the oven and add the butter, allowing it to melt completely and coat the bottom of the dish.
Pour the batter into the melted butter in the baking dish.
Return the dish to the oven and bake for 20-25 minutes, or until the pancake is puffed and golden brown.
Once baked, remove from the oven and let it cool slightly. Dust with powdered sugar and serve with lemon wedges if desired.