Preheat the oven to 400 F. Grease a 9x13" baking pan lightly and set it aside. In a large bowl, whisk together the flour, sugar and salt. Then add the milk and vanilla. Next, whisk in each egg one at a time, whisking to combine for each one.
Place the 3 tbsp. of butter into the prepared pan and place it into the preheated oven for just a couple of minutes, until the butter has melted. Then remove the pan from the oven, pour in the batter right over the butter, and place the pan back in the oven for 17-20 minutes, until it has puffed nicely and the edges are golden brown. Remove it from the oven and let it sit for a few minutes (it will deflate as it sits).
While the German pancake is baking, start preparing the apples. Heat the 2 tbsp. of butter in a large skillet over medium heat. Place the apple slices into a large bowl and toss them in the sugars and cinnamon. Then pour them into the skillet. Cook, stirring around often, for 5-7 minutes, until the apples have softened and the sugars have caramelized slightly.
Slice the pancake into 6 equal sized squares and serve with the apple slices atop it.
