1. Preheat your oven to 350 F (175 C). Grease and flour a 9×5-inch loaf pan, or line it with parchment paper, leaving an overhang on the long sides.

2. In a large mixing bowl, whisk together the 1 1/2 cups all-purpose flour, 1/2 cup granulated sugar, baking powder, baking soda, salt, 1 teaspoon ground cinnamon, and nutmeg until well combined.

3. In a separate medium bowl, whisk the egg, 1/2 cup milk, melted butter, and vanilla extract until smooth.

4. Pour the wet ingredients into the dry ingredients. Stir gently with a spatula until just combined. Do not overmix; a few lumps are fine. Gently fold in the diced apples.

5. For the crumb topping: In a small bowl, combine the 1/2 cup all-purpose flour, 1/4 cup granulated sugar, brown sugar, and 1/2 teaspoon cinnamon. Add the cold, cubed butter. Using your fingertips or a pastry blender, work the butter into the dry ingredients until the mixture resembles coarse crumbs.

6. Pour the apple bread batter into the prepared loaf pan, spreading it evenly. Sprinkle the crumb topping generously over the top of the batter. Place the loaf pan in the preheated oven and bake for 45-55 minutes, or until a wooden skewer or toothpick inserted into the center of the loaf comes out clean. If the topping starts to brown too quickly, loosely tent it with aluminum foil.

7. Once baked, remove the loaf from the oven and let it cool in the pan for about 10-15 minutes. Then, carefully lift it out using the parchment paper overhang or invert it onto a wire rack to cool completely. If desired, whisk together the powdered sugar and 1-2 tablespoons of milk for the glaze. Drizzle the glaze over the cooled loaf just before serving.