Preheat the oven to 350°F. Grease a 9x9” baking dish with non-stick cooking spray. If you'd like to lift the cooked apple crumb bars out of the pan, you can line the pan with parchment paper. Set aside.
To make the shortbread crust: Use the paddle attachment on a stand mixer and add the butter, sugar and brown sugar. Beat on medium speed until smooth. Add vanilla and mix to combine. Add flour and salt and mix until incorporated and mixture begins to come together.
Press the dough into an even layer in the bottom of the prepared pan taking care to push in into the corners as well. Use a fork to poke several holes into the bottom of the crust. Place on the center rack of your preheated oven and bake for 15 minutes until it's a light golden brown. Remove from the oven and place on a wire rack.
While the crust is cooking, prepare the apple layer and topping.
Make the filling: In a large mixing bowl combine your sliced apples, sugar, cornstarch, brown sugar, cinnamon, nutmeg, salt and cloves. Mix until the apples are well coated, then add your lime juice and stir gently to combine.
Make the Crumb Topping: In a medium sized mixing bowl combine the oats, flour, brown sugar, cinnamon and salt. Add butter and mix in using a fork or pastry blender until crumbly in texture. Note: You can save washing a dish if you use your stand mixing bowl to combine these ingredients.
Assembly:Spoon the apple mixture onto the pre-baked crust. You'll likely need to use clean hands to spread the apples out evenly.
Spoon the oat topping evenly over the top of the apples. Place back into the heated oven on the center rack and bake for 55 minutes. If the topping starts to get too brown, you can loosely cover it with aluminum foil.
When done baking, remove from the oven and place on a wire cooling rack to cool.