Preheat your oven to 350 degrees Fahrenheit and prepare a 12-cup muffin tin with paper liners.
Add the flour, sugar, baking powder, cinnamon, nutmeg and salt to a large bowl and combine with a wire whisk.
Add the unpeeled diced apples to the flour mixture and toss well to ensure the apples are well coated. This will help them remain distributed throughout the muffin batter when baking and keep them from settling at the bottom of the muffins.
Whisk the milk, egg and oil together in a small bowl or measuring cup and add the mixture to the dry ingredients.
Fold the wet and dry ingredients together gently just until no streaks of flour remain.
Spoon the muffin batter into the muffin cups, dividing the batter between them as evenly as possible.
Combine the ingredients for the crumble topping together in a small bowl until the mixture resembles coarse crumbs.
Top each unbaked muffin with a spoonful of crumb topping and bake the muffins at 350 degrees for about 23-25 minutes or until the muffins are golden brown and a toothpick inserted into one of the muffins comes out clean.
Let the muffins cool in their tins for about 5 minutes before removing them to a wire rack to cool completely.