Preheat oven to 350°F (175°C). Grease or line an 8x8-inch baking dish.

Make the crumb topping: In a small bowl, mix flour, brown sugar, and cinnamon. Cut in the cold butter with a fork until mixture is crumbly. Chill while preparing cake.

In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg.

In a large bowl, beat butter and both sugars until light and fluffy. Add eggs one at a time, mixing well. Stir in sour cream and vanilla.

Gradually add the dry ingredients to the wet until just combined. Fold in diced apples.

Pour batter into the prepared pan and smooth the top. Sprinkle with crumb topping.

Bake for 40–45 minutes or until a toothpick inserted in the center comes out clean.

While baking, make the drizzle: In a small saucepan over medium heat, cook apples, butter, brown sugar, cinnamon, and a splash of water until apples are tender and the mixture is syrupy, about 5–7 minutes.

Let cake cool slightly before drizzling warm cinnamon apple sauce over the top.