Preheat the oven to 350 degrees F (175 degrees C).

In a large bowl, stir together flour, sugar, baking powder, and salt. Cut in butter with 2 knives or a pastry blender until lumps are no larger than peas. Stir in beaten egg lightly, allowing flour mixture to stay somewhat crumbly.

Sprinkle 1/2 of the flour mixture in an even layer in the bottom of a 9x13-inch baking dish. Pack down into a solid crust. Spread cranberry sauce over crust. Crumble remaining flour mixture over cranberry sauce.

Bake in the preheated oven until the top is golden brown, about 40 minutes. Cool completely before slicing into 15 bars.