Prepare the Apple Filling:
Peel, core, and slice the apples. In a saucepan, combine apples, sugar, cinnamon, lemon juice, and vanilla. Cook over medium heat until apples soften but still hold their shape (5-7 minutes). Stir in flour to thicken the filling.
Make the Shortbread Crust:
Preheat oven to 350°F (175°C). Beat together the butter and sugar until fluffy. Add egg and vanilla, then mix in flour, baking powder, and salt to form a dough. Press about two-thirds of the dough into a greased 9×13-inch pan.
Bake the Crust:
Bake the crust in the oven for 15-20 minutes, until golden around the edges.
Assemble the Squares:
Once the crust has cooled slightly, spread the apple filling evenly over the crust. Roll out the remaining dough and place it over the apples. For a rustic look, crumble the dough on top.
Add Crumble Topping:
Combine flour, brown sugar, cinnamon, and salt. Add cold butter, mixing until the topping is crumbly. Sprinkle over the top of the assembled squares.
Bake the Squares:
Bake for 35-40 minutes at 350°F (175°C), until the top is golden brown and apples are bubbling.
Cool and Serve:
Allow the squares to cool for 15 minutes before cutting into squares. Serve warm or at room temperature with your favorite toppings.