For the crisp: Peel and core the apples. Roughly chop into 1-inch chunks and toss with the sugar in a large bowl. Cover with plastic wrap and refrigerate 8 hours or up to overnight.
Preheat the oven to 350 degrees F. Butter a 13-by-9-inch or 2-quart baking dish.
Drain the apples from their liquid and return the apples to the bowl. Add the cinnamon, nutmeg, salt, cloves and ginger and toss well. Using a rubber spatula, mix in the walnuts, maple syrup and half the cream cheese. Spread evenly in the prepared baking dish, then dot the mixture with the remaining cream cheese.
For the topping: Mix together the crushed gingersnaps, oats, sugar and melted butter. Spread the topping evenly across the crisp and bake until bubbly, 25 to 30 minutes. Serve hot or at room temperature with ice cream.