1. Preheat oven to 350°F (175°C). Grease and flour a 9×13 inch baking pan, or line it with parchment paper.
2. In a medium bowl, whisk together flour, baking soda, salt, cinnamon, and nutmeg for the cake. Set aside.
3. In a large bowl, cream softened butter and granulated sugar with an electric mixer until light and fluffy.
4. Beat in eggs one at a time, then stir in vanilla extract.
5. Gradually add the dry ingredients to the wet ingredients, alternating with the buttermilk, beginning and ending with dry ingredients. Mix until just combined, being careful not to overmix.
6. Gently fold in the diced apples to the cake batter.
7. Pour the batter into the prepared baking pan and spread evenly.
8. In a separate medium bowl, combine flour, brown sugar, cinnamon, and salt for the crumb topping. Whisk to combine.
9. Cut in the cold butter pieces using a pastry blender, a fork, or your fingertips until the mixture resembles coarse crumbs.
10. Sprinkle the crumb topping evenly over the cake batter.
11. Bake for 40-45 minutes, or until a wooden skewer inserted into the center comes out clean.
12. Let the cake cool in the pan on a wire rack before slicing and serving.