Preheat the oven to 450 degrees F. In a large ovenproof skillet (preferably with curved sides), melt 2 tablespoons of the butter over medium heat.
Add the apple slices and cook, stirring, until tender, about 10 minutes.
Add 2 tablespoons of the brown sugar and stir to combine.
In a medium bowl, whisk together the eggs, sugar, salt, milk, and flour.
Pour this batter over the apples in the skillet, transfer to the oven, and bake until puffy, about 10 minutes. Meanwhile, in a small bowl, mix the cinnamon and remaining 2 tablespoons brown sugar.
Cut the remaining tablespoon of butter into pieces. When the pancake puffs, remove from the oven, dot with butter, sprinkle with cinnamon sugar, and return to the oven to bake until browned, about 10 minutes more. As the pancake comes out of the oven, squeeze the lemon wedges over the top.
