Preheat the oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a large bowl, whisk together 2 cups flour, 3/4 cup granulated sugar, brown sugar, baking powder, baking soda, salt, cinnamon, and nutmeg until well combined.
In a separate medium bowl, beat the egg. Add the buttermilk, vegetable oil, vanilla extract, and melted butter. Mix until combined.
Pour the wet ingredients into the dry ingredients and gently fold together until just combined. Do not overmix; the batter should be slightly lumpy.
Fold in the diced Granny Smith apples evenly into the batter.
To make the crumb topping, combine 1/2 cup granulated sugar, 1/3 cup flour, and 1/2 teaspoon cinnamon in a small bowl. Cut in the cold cubed butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Spoon the batter evenly into the prepared muffin cups, filling each about 3/4 full.
Sprinkle the crumb topping generously over each muffin.
Bake for 18 to 22 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and let them cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.