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 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, swirling it around to coat the bottom. Allow the butter to melt completely.
Pour the batter into the hot baking dish over the melted butter.
Return the dish to the oven and bake for 20-25 minutes, or until the pancake is puffed and golden brown.
Remove from the oven and let it cool for a minute. Dust with powdered sugar and serve with fresh lemon juice or maple syrup.