Beat the eggs. Meanwhile, whisk the eggs in a large bowl.
Add milk. Add the milk and vanilla, and beat with the whisk until well combined.
Add the dry ingredients. Using a sifter or a fine mesh strainer, sift the flour and salt over the egg mixture in the bowl. Then, stir it all together until you have a smooth batter. Set the batter aside to rest for 5 minutes.
Prepare to bake. While the batter rests, preheat the oven to 400°F. Add the butter to a 9x13 rectangular dish. Place the baking dish in the oven and allow the butter to melt completely, about 3-5 minutes.
Bake the pancake. Carefully remove the baking dish from the oven and pour in the pancake batter. Bake the pancake for 20-25 minutes or until the edges are brown and puffy.
Serve. Remove from the oven and serve your German pancake while still warm, dusted with powdered sugar.
Notes
Sifting is optional. You can absolutely just whisk the flour and salt together before adding them to the egg mixture.