Prepare the shortbread and topping:

1. Preheat the oven to 375ºF and place oven racks in the lowest and middle parts of the oven. Butter or oil an 8-inch square (or similar size) baking dish. Cut a strip of parchment to fit inside the dish with ends long enough to hang over the edges. Line the baking dish with the parchment and set aside.
2. In a medium bowl, whisk together the melted butter, granulated sugar, brown sugar, baking powder, vanilla, cinnamon and salt . Stir in the flour until just combined.
3. Sprinkle ⅔ of the crumb mixture into the prepared baking dish as evenly as possible. Using a flat-bottomed measuring cup or your hands, press the mixture into an even layer. Bake the crust in the preheated oven on the lowest rack until it’s lightly golden on the edges with a matte appearance in the middle, about 12 minutes. Remove and set aside until ready to use.
4.  
5. Meanwhile, make the filling: In a large pot, combine the apples, granulated sugar, cinnamon, nutmeg, clove, salt, ¼ cup cider and vanilla.
6. Turn the heat to medium and begin to cook the apples. Stir occasionally to make sure the apples cook evenly. Cook until the apples have softened, about 6 minutes, making sure not to cook off all of the liquid. If the liquid does cook off quickly, add a splash more apple cider to the pot.
7. In a small bowl, create a slurry by whisking together the cornstarch and the remaining 1 tablespoon of apple cider.
8. Pour the cornstarch slurry into the apples and stir together until dissolved. Continue cooking until the mixture is thickened, about 1-2 minutes. 
9. Transfer the apple filling onto the par-baked crust and spread into an even layer. Sprinkle the remaining crumb mixture evenly on the top.
10. Bake on the middle rack until the filling is slightly puffed up and the crumb mixture is a light golden color, 30 to 35 minutes.
11. Transfer to a wire rack and let cool completely. 
12. Cut into 16 pieces and serve. Store at room temperature in a covered container for up to 1 day or in the refrigerator for up to 2 to 3 days.