Preheat oven: Set to 350°F (175°C). Grease a 12-cup muffin tin or line with paper liners.
Prepare apple filling: In a large bowl, toss diced apples with granulated sugar, brown sugar, cinnamon, nutmeg, lemon juice, and cornstarch until evenly coated.
Make crumble topping: In another bowl, combine oats, flour, brown sugar, cinnamon, and salt. Stir in melted butter until crumbly. Fold in nuts if using.
Assemble bites: Spoon about 2 tablespoons of apple mixture into each muffin cup, pressing lightly. Top with 1-2 tablespoons of crumble, pressing gently.
Bake: Bake for 20-25 minutes, until the topping is golden and apples are tender. Test with a toothpick for doneness.
Cool and serve: Cool in the tin for 10 minutes, then transfer to a wire rack. Serve warm with ice cream or caramel sauce.