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 pour the melted butter into the dish, swirling it around to coat the bottom evenly.
Immediately pour the batter into the hot baking dish over the melted butter.
Bake for 20-25 minutes or until the edges are puffed and golden brown. The center should be set and slightly jiggly.
Remove from the oven and let it cool for a minute. Cut into squares and serve warm, dusted with powdered sugar and with lemon wedges on the side. Drizzle with maple syrup if desired.