Prepare a grill for indirect heat. If using a charcoal grill, build the hot coals on one side only. If using a gas grill, heat one side only to medium-high heat.
Add the apples to a 10- to 12-inch cast-iron skillet, filling it almost to the top. Combine the flour, oats, sugars, cinnamon and salt in a large bowl. Cut the butter into small cubes and add to the flour mixture. Using your hands, press the butter into the dry ingredients until it forms a course crumble. Sprinkle evenly over the apples.
Place the skillet over indirect heat, cover the grill and cook until the apples are completely tender when pierced with a knife and the crumble is golden brown and crispy, 30 to 40 minutes. Serve warm or at room temperature.
(Alternatively, you can bake this in an 8-inch square cake pan in a 350 degrees F oven for 45 minutes to 1 hour.)