In a 10 inch cast-iron skillet or non-stick pan melt the butter with 3 tablespoons of the brown sugar. Add the apple slices and cook for 4-6 minutes, stirring occasionally.
In a large bowl whisk together the eggs, flour, milk, cinnamon, salt, vanilla and remaining tablespoon of brown sugar.
Pour the batter over the cooked apple mixture. Transfer the skillet to the oven. Bake until dark golden brown and puffed around the edges, about 15 minutes.
While the pancake is in the oven, make the glaze. Combine the powdered sugar, milk and cinnamon in a bowl and stir until thoroughly combined.
After the pancake comes out of the oven, let it cool for 5 minutes (it will deflate a bit). Drizzle the glaze over the pancake and top with additional cooked apples if desired.