Preheat oven to 350 degrees. Lightly coat the inside of a 9x9-inch or similarly sized baking dish with cooking spray, then set aside.
Peel and core the apples, then either slice or chop into bite-sized pieces. (I find the perfect thickness is about 1/2".) In a large mixing bowl, combine apples with granulated sugar, lemon juice, cinnamon, and a pinch of sea salt. Toss to coat, then spread the mixture in an even layer across the bottom of the baking dish.
In the same mixing bowl, combine the oats, brown sugar, flour, cinnamon, nutmeg, and another pinch of sea salt. Whisk or stir with a fork to blend well.
Cut the butter into small pieces. Using a pastry blender, two forks, or just your hands, cut and press the butter pieces into the oat-flour mixture, working until the entire mixture is crumbly and mostly pea-sized pieces of butter remain.
Spread the topping evenly over the apples, then transfer to the oven and bake for 40-50 minutes. The topping should be golden brown and the apples should give way easily when pierced with a fork.
Serve warm, with vanilla ice cream and caramel sauce if desired.