In a medium bowl, whisk together 1 cup flour, brown sugar, 1/2 teaspoon cinnamon, and 1/4 teaspoon nutmeg. Add the cold, cubed butter and cut it in with a pastry blender or your fingertips until you have coarse crumbs. Cover and refrigerate while you make the other components.

In a medium bowl, combine the diced apples with 2 tablespoons granulated sugar, lemon juice, 1 teaspoon cinnamon, 1/4 teaspoon nutmeg, and 1 tablespoon flour. Stir until the apples look evenly coated and slightly glossy. Set aside.

Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with cupcake liners.

In a medium bowl, whisk together 1 1/2 cups flour, baking powder, baking soda, and salt.

In a large bowl, cream the softened butter and 3/4 cup granulated sugar until light and fluffy, about 3–5 minutes.

Beat in the eggs one at a time, mixing until each disappears before adding the next. Stir in the vanilla extract.

In a small bowl, whisk the sour cream (or yogurt) with the milk until smooth.

Add the dry ingredients to the butter mixture alternating with the sour cream mixture, beginning and ending with the dry ingredients. Mix just until no dry flour remains.

Spoon about 2 tablespoons of batter into each liner. Add about 2 tablespoons of apple filling over the batter, then sprinkle the chilled crumble topping evenly over the apples.

Bake for 20–25 minutes, until a toothpick inserted into the center comes out clean.

Let the cupcakes cool in the tin for a few minutes, then transfer to a wire rack to cool completely. Drizzle with caramel sauce and/or dust with powdered sugar.