Heat the oven to 375 degrees. Coat a 1 1/2-quart shallow baking dish with nonstick cooking spray.
Toss the apples, cranberries, 1 cup sugar, and 2 teaspoons apple pie spice in a large bowl. Whisk 1/2 cup sour cream and egg in a small bowl until blended. Stir into the apple mixture. Place in the baking dish.
Combine oats, flour, ¾ cup sugar, 1 teaspoon allspice, and ½ cup sour cream in a medium bowl until crumbly. Sprinkle over the fruit and then drizzle with the butter.
Bake for 45 to 55 minutes or until the topping is golden brown, the juices are bubbly, and the fruit is tender. Serve warm or at room temperature.