Place a 5-quart enameled braiser or a large cast-iron skillet in the oven and preheat to 425 degrees F.
In a small bowl, whisk together the eggs, milk and vanilla until smooth. In a separate medium bowl, whisk together the flour, granulated sugar, salt and lemon zest. Add the wet ingredients to the dry ingredients; whisk until fully incorporated and smooth. Allow the batter to rest for 5 minutes.
Remove the pan from the oven and add the butter, swirling until melted. Pour the batter into the center of the pan, then return to the oven. Bake until the pancake is puffed and brown around the edges and set in the center, 20 to 25 minutes.
Remove the pan from the oven and dust the pancake with powdered sugar. (The pancake will start to collapse as soon as it's out of the oven.) Serve topped with berries and whipped cream, or simply with jam or syrup.