Over medium heat, brown the butter on the stove in a small pan. Stir butter to keep it from burning until it has a nutty aroma and brown specks appear. Remove from heat.
In a large mixing bowl, combine flour, brown sugar, brown butter, and oats. Measure out 1 cup of the mixture to reserve for the topping. Set aside. Press the remainder of the mixture into an ungreased cast iron skillet (or pie pan). Set skillet aside.
In a large bowl, mix together the diced apples, lemon juice, sugar, flour, and cinnamon until apples are evenly coated. Pour into skillet, mounding apples toward center.
Sprinkle reserved crumbs evenly on top.
Bake for 45-50 minutes or until top and crust is a deep golden brown color. Transfer to cooling rack to cool.