Preheat your oven to 375°F (190°C) and line a 12-cup muffin tin with paper liners or spray with non-stick cooking spray.
Prepare the crumb topping by combining flour, brown sugar, cinnamon, and salt in a medium bowl. Add the cold cubed butter and use your fingers or a pastry cutter to work the mixture until it resembles coarse crumbs. Place in the refrigerator while you prepare the muffin batter.
In a large bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and salt until well combined.
In a separate bowl, mix the melted butter with both sugars until smooth. Add the eggs one at a time, beating well after each addition. Stir in the milk and vanilla extract.
Pour the wet ingredients into the dry ingredients and gently fold together using a rubber spatula or wooden spoon just until combined. The batter will be thick – don’t overmix or your muffins will be tough!
Fold in the diced apples until evenly distributed throughout the batter.
Divide the batter evenly among the prepared muffin cups, filling each about ¾ full.
Remove the crumb topping from the refrigerator and sprinkle generously over each muffin, gently pressing it into the batter slightly.
Bake for 18-22 minutes or until a toothpick inserted in the center comes out clean or with just a few moist crumbs. The tops should be golden brown and slightly domed.
Allow the muffins to cool in the pan for 5 minutes before transferring to a wire rack to cool completely.