Preheat oven to 350°F. Coat an 8 x 8-inch baking pan with vegetable cooking spray. Line with heavy-duty foil, leaving an overhang on two sides to facilitate removal of bars from pan. Coat foil with cooking spray.
Mix flour, oatmeal, sugar, and salt in a medium bowl. Stir in butter with a fork until well mixed and clumps form, and then spread half the oatmeal mixture over foiled pan bottom, pressing to form a thin crust. Spread apple butter over crust and then sprinkle remaining oatmeal mixture on top.
Bake until crisp and golden brown, 30 to 40 minutes. Cool to room temperature. Use foil “handles” to remove bars from pan. Cut into squares and serve.