Prep the pan and oven. Heat the oven to 350°F (175°C). Grease and line a 9-inch square pan (or 9-inch round springform) with parchment, leaving a little overhang for easy lifting.
Prep the apples. Peel (optional), core, and dice the apples into small 1/2-inch pieces. Toss with 1 tablespoon lemon juice, 1 teaspoon cinnamon, and a pinch of brown sugar.
Set aside.
Make the crumb topping. In a bowl, mix 1 cup flour, 3/4 cup light brown sugar, 1 teaspoon cinnamon, and a pinch of salt. Stir in 6 tablespoons melted butter until clumps form. Squeeze with your fingers to make big crumbs.
Chill while you make the batter.
Combine dry ingredients for the cake. In a large bowl, whisk 1 1/4 cups flour, 3/4 cup granulated sugar, 2 teaspoons baking powder, 1/2 teaspoon salt, and 1/2 teaspoon cinnamon (plus nutmeg if using).
Mix wet ingredients. In another bowl, whisk 2 eggs, 3/4 cup milk (or buttermilk), 1/3 cup sour cream, 1/4 cup oil, 4 tablespoons softened butter, and 2 teaspoons vanilla until smooth.
Make the batter. Pour the wet into the dry and whisk gently until just combined. The batter should be thick but spreadable. Don’t overmix.
Assemble the layers. Spread the batter evenly in the pan.
Scatter the spiced apple pieces over the top in an even layer. Sprinkle the chilled crumb mixture over everything, pressing some larger clusters together for texture.
Bake. Bake for 40–50 minutes, until the crumb is golden and a toothpick inserted in the center comes out with moist crumbs but no wet batter. If the top browns too fast, tent loosely with foil for the last 10 minutes.
Cool. Let the cake cool in the pan for at least 30 minutes.
Lift out using the parchment and cool to just warm before slicing. The crumb sets as it cools.
Optional glaze. Whisk 1/2 cup powdered sugar with 1–2 teaspoons milk and a few drops of vanilla. Drizzle over the cooled cake for a light finish.