Set the oven rack to the center position. Heat to 375ºF (191ºC).

Peel, core, and cut the apples into ½-inch thick slices.

In a large bowl, stir to combine sliced apples, granulated sugar, brown sugar, cinnamon, nutmeg, salt, lemon zest, and lemon juice.

Heat a large skillet over medium heat. Once hot, add the butter and the apple mixture. Saute until crisp-tender, and most of the moisture is released, about 15 to 20 minutes.

Lightly butter the bottom and sides of an 8 by 8-inch baking dish. Evenly spread the cooked apples inside the dish.

In a medium bowl, whisk together the flour, rolled oats, brown sugar, cinnamon, salt, and nutmeg.

Cut cold butter into ¼-inch cubes and add to the flour mixture. Use fingers to break the butter into the dry ingredients, pressing together to create large pebble-shaped pieces of crumbly topping, about the size of a dime. Evenly sprinkle the topping over the apples.

Bake until the topping is golden brown and crisp, about 30 to 35 minutes. Transfer to a wire rack and cool for 10 to 15 minutes.

Serve warm with desired toppings.