Preheat the Oven:
Set your oven to 350°F (175°C) and line a 9×9-inch baking pan with parchment paper, leaving an overhang on the sides for easy removal of the bars.
Make the Shortbread Crust:
In a medium mixing bowl, beat the room-temperature butter and brown sugar until smooth and fluffy. Stir in the vanilla extract. Gradually add the flour, mixing until it forms a crumbly dough. Press this dough evenly into the lined baking dish to create a firm crust. Bake for 15 minutes, or until the edges turn a light golden brown. Set aside to cool slightly.
Prepare the Apple Filling:
In another bowl, mix the sliced apples with flour and granulated sugar until well-coated.
Create the Crumble Topping:
In a separate bowl, combine brown sugar, granulated sugar, flour, cinnamon, and salt. Add the chilled butter cubes and cut them in with a pastry cutter or fork until the topping resembles coarse crumbs.
Assemble the Bars:
Spread the apple filling evenly over the shortbread crust. Sprinkle the crumble topping over the apples, pressing it down gently to ensure it sticks.
Bake:
Place the pan in the oven and bake for 40-45 minutes, or until the topping is golden brown and the apple filling is bubbling around the edges.
Cool and Slice:
Leave the bars in the pan to cool on a wire rack. Once fully cooled, lift them out using the parchment paper and cut into squares. Serve warm or at room temperature.