Let's cook.
Preheat your oven to 375°F (190°C).
Prepare the apple filling: Peel, core, and slice the apples into 1/4-inch thick pieces. In a large bowl, toss the apple slices with 1/2 cup of brown sugar, 1 teaspoon of ground cinnamon, 1/4 teaspoon of ground nutmeg, and 1 tablespoon of lemon juice until evenly coated.
Prepare the crumble topping: In a separate medium bowl, combine 1/2 cup of all-purpose flour, 1/2 cup of rolled oats, the remaining 1/2 cup of brown sugar, the remaining 1/2 teaspoon of ground cinnamon, and 1/4 teaspoon of salt. Cut in the 1/2 cup of cold, cubed unsalted butter using your fingers or a pastry blender until coarse crumbs form.
Assemble the crumble: Pour the apple mixture into a 10-inch oven-safe skillet. Evenly sprinkle the prepared crumble topping over the apples.
Bake the crumble: Bake for 30-40 minutes, or until the apples are tender when pierced with a fork and the topping is golden brown and bubbly around the edges.
Serve: Let the skillet apple crumble cool for a few minutes before serving warm, perhaps with a scoop of vanilla ice cream or a dollop of whipped cream.
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