1. Prepare the Crumb Topping: In a medium bowl, combine 1/2 cup of the all-purpose flour, 1/4 cup granulated sugar, 1/4 cup brown sugar, 1/2 teaspoon cinnamon, and 1/4 teaspoon nutmeg. Add the cold, cubed butter. Using your fingertips or a pastry blender, work the butter into the dry ingredients until coarse crumbs form. The mixture should resemble wet sand with some pea-sized pieces of butter still visible. Place this bowl in the refrigerator while you prepare the cake batter.

2. Preheat Oven and Prepare Pan: 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 longer sides to easily lift the loaf out later.

3. Combine Dry Ingredients for Cake: In a large mixing bowl, whisk together the remaining 1 cup all-purpose flour, 1/4 cup granulated sugar, 1/4 cup brown sugar, 1/2 teaspoon cinnamon, 1/4 teaspoon salt, and 1 teaspoon baking soda. Make sure there are no lumps and all ingredients are evenly distributed.

4. Mix Wet Ingredients for Cake: In a separate medium bowl, whisk together the egg, sourdough discard, milk, vanilla extract, and lemon juice until well combined and smooth. The lemon juice helps activate the baking soda, contributing to the loaf’s rise and tender crumb.

5. Combine Wet and Dry Mixtures, Add Apples: Pour the wet ingredients into the dry ingredients. Stir gently with a spatula or wooden spoon until just combined. Be careful not to overmix; a few streaks of flour are okay. Fold in the finely diced apples. The batter will be thick.

6. Assemble and Bake: Pour the cake batter into the prepared loaf pan, spreading it evenly with your spatula. Retrieve the chilled crumb topping from the refrigerator and sprinkle it generously and evenly over the top of the batter.

7. Bake the Loaf: Place the loaf pan in the preheated oven and bake for 45-55 minutes. The loaf is done when a wooden skewer or toothpick inserted into the center comes out clean or with moist crumbs, but no wet batter. The crumb topping should be golden brown and crisp.

8. Cooling: Once baked, remove the loaf from the oven and let it cool in the pan for about 15 minutes. Then, use the parchment paper overhang or a knife to carefully remove the loaf from the pan and transfer it to a wire rack to cool completely before slicing and serving. This allows the loaf to set properly and prevents it from becoming gummy.