Preheat oven to 350 degrees and place oven rack in bottom third of oven.
Make the Apple Filling: Stir the cornstarch and lemon juice together in a large bowl until the cornstarch is dissolved. Add the apples, sugar, salt, cinnamon and nutmeg and toss to combine. Pour mixture into an 8-inch-square (or other 2-quart) baking dish.
Make the Almond Crisp Topping: In a medium bowl, whisk together the flour, brown sugar, almond pieces, salt, cinnamon and nutmeg. Use a pastry blender (or your fingertips) to quickly incorporate the butter into the dry ingredients until the mixture is the consistency of coarse crumbs. Sprinkle the topping evenly over the apple filling.
Bake for 50 to 55 minutes, or until the topping is golden brown, the juices are bubbling and the apples are tender.