Preheat the oven to 350°F and grease an 8x8 baking pan.
In a medium bowl, mix 3/4 cup flour, granulated sugar, baking powder, 1/2 teaspoon cinnamon, and salt.
In another bowl, beat 4 tablespoons butter with the egg until smooth, then stir in the dry mixture until just combined.
Fold the diced apples into the batter and spread it evenly in the prepared pan.
For the crumb topping, combine the remaining 1/4 cup flour, brown sugar, and 1/2 teaspoon cinnamon. Cut in the remaining 2 tablespoons butter until the mixture forms coarse crumbs.
Sprinkle the crumb topping over the batter and bake for 30 to 35 minutes until a toothpick comes out clean.
Let the cake cool slightly, then drizzle the caramel sauce over the top before slicing.