Prepare the Streusel Topping: In a medium mixing bowl, whisk together the rolled oats, packed brown sugar, flour, salt, and cinnamon until evenly combined.
Incorporate the Butter: Add the chilled, cubed butter to the oat mixture. Cut it into the dry ingredients or work it in with your fingertips until the mixture forms coarse clumps.
Chill the Streusel: Cover the bowl and refrigerate the topping while preparing the crust and apple filling. The streusel can also be prepared up to one day ahead and kept chilled.
Combine the Crust Dry Ingredients: In a large mixing bowl, whisk together the all-purpose flour, salt, and cinnamon. Set the mixture aside.
Cream the Butter and Sugars: Using a stand mixer fitted with a paddle attachment, beat the softened butter, granulated sugar, and packed brown sugar until the mixture becomes creamy.
Finish the Crust Dough: Add the vanilla extract and mix to combine. With the mixer running on low speed, gradually add the flour mixture, mixing until the ingredients form a cohesive dough.
Press the Crust into the Pan: Transfer the dough to a 9 × 13-inch oven-safe baking dish. Press it evenly across the bottom to create the shortbread base. Refrigerate for 20 minutes; do not skip this chilling step.
Preheat the Oven: Heat the oven to 375°F (approximately 190°C) while the crust chills.
Prebake the Crust: Bake the chilled shortbread crust for 18 minutes. Remove the dish from the oven and allow the crust to cool while preparing the apple filling. Reduce the oven temperature to 350°F (approximately 175°C).
Season the Apples: Place the peeled, cored, thinly sliced apples in a large mixing bowl. Add the granulated sugar, ground cinnamon, and optional nutmeg, tossing until the slices are evenly coated.
Prepare the Thickener: In a small bowl, whisk the lemon juice and cornstarch together until combined. Add this mixture to the seasoned apples and stir to distribute it throughout the filling.
Cook the Apple Filling: Transfer the apple mixture to a large saucepan and cook over medium heat for 5–8 minutes, stirring occasionally, until the apples begin to soften. Add water as needed to keep the apples from sticking, scorching, or burning in the pan. Avoid overcooking, as the apples will continue to soften in the oven. Layer the Apples over the Crust: Spread the cooked apple mixture evenly over the prebaked shortbread crust, distributing the slices across the surface.
Add the Streusel Topping: Remove the chilled streusel from the refrigerator and scatter it evenly over the apples, covering the filling with the oat mixture.
Bake the Apple Pie Bars: Place the assembled dish in the oven at 350°F (approximately 175°C) and bake for 30–35 minutes, until the topping is golden and the layers are baked through.
Cool and Slice: Remove the dish from the oven and allow the bars to cool before cutting. Slice into 12 large bars and serve as they are or alongside vanilla bean ice cream.