For the crisp: Preheat the oven to 400 degrees F. Spray an 8-inch square baking dish with nonstick cooking spray.
Mix the flour, brown sugar and salt in a bowl. Use a pastry blender, two knives, or a food processor to cut in the butter until the size of peas. Add the oats and combine, taking care to not break up the oats too much. Set aside.
For the filling: In a bowl, combine the squash, apples and cranberries and toss with the granulated sugar, cornstarch, pumpkin pie spice and salt. Transfer to the prepared baking dish. Top with the crisp mixture. Bake until the top is golden brown and crispy, 50 to 55 minutes.