Preheat the oven to 375 degrees F (190 degrees C). Lightly butter an 8-inch square baking dish.

Make the cake: Sift flour, sugar, baking powder, and salt into a mixing bowl. Cut in butter with 2 knives or a pastry blender until mixture is crumbly.

Whisk cream and egg together in a small bowl; add to flour mixture and gently mix until a soft dough forms. Press into the prepared baking dish. Layer apples over top in neat rows, overlapping slightly.

Make the streusel topping: Whisk brown sugar, flour, and cinnamon together in a small bowl. Cut in butter until mixture is crumbly. Sprinkle topping over apples.

Bake in the preheated oven until apples have softened and topping is golden brown, about 25 minutes.