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 to easily lift the loaf out later.

2. In a large mixing bowl, whisk together the 1 1/2 cups all-purpose flour, granulated sugar, baking powder, baking soda, ground cinnamon, and salt. Make sure there are no lumps and everything is evenly distributed.

3. In a medium bowl, whisk together the large egg, milk, melted butter, and vanilla extract until well combined. The mixture should be smooth and uniform.

4. Pour the wet ingredients into the bowl with the dry ingredients. Stir gently with a spatula or wooden spoon until just combined. Be careful not to overmix; a few lumps are perfectly fine. Gently fold in the diced apples until they are evenly distributed throughout the batter.

5. In a small bowl, combine the 1/4 cup all-purpose flour, packed light brown sugar, and 1/2 teaspoon ground cinnamon. Add the cold, cubed butter. Use your fingertips or a pastry blender to cut the butter into the dry ingredients until the mixture resembles coarse crumbs.

6. Pour the batter into your 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 35-40 minutes, or until a wooden skewer or toothpick inserted into the center of the loaf comes out clean. The top should be golden brown and the crumbs nicely toasted.

7. Once baked, remove the loaf from the oven and let it cool in the pan for about 10-15 minutes on a wire rack. After 10-15 minutes, use the parchment paper overhang or carefully invert the loaf onto the wire rack to cool completely before slicing and serving.