Preheat oven to 375°F (190°C). Line a 12-count muffin pan with 12 liners and set aside.
In a large mixing bowl, whisk together the flour, baking powder, salt, ground cinnamon, and nutmeg. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using an electric mixer, cream the butter, brown sugar, and granulated sugar together for 3-4 minutes or until light and fluffy. Mix in the eggs, vanilla, and sour cream until well combined, stopping to scrape down the sides of the bowl as needed.
Add the dry ingredients and the milk and mix until just combined. Fold in the chopped apples.
Evenly distribute the batter between all 12 muffin liners in the prepared muffin pan, filling them all the way to the top of the liners.
Remove the crumb topping from the refrigerator and sprinkle on top of each one, gently press it down if needed.
Bake at 375°F (190°C) for 18-22 minutes or until the tops of the muffins are set and a toothpick inserted into the center comes out clean. Remove from the oven and cool in the pan for 5 minutes, then carefully remove the muffins from the pan and transfer to a wire rack to cool completely.