Combine orange juice, apples, cranberries, white sugar, brown sugar, and pumpkin pie spice in a saucepan over medium-high heat. Bring to a boil, reduce heat, and simmer until apples are tender and sauce has thickened slightly, 20 to 25 minutes.
Transfer sauce to a dish; stir in softened butter and refrigerate for 1 to 2 hours. Sauce will continue to thicken.
