Combine the apples, lemon juice, or cider and the 1/3 cup of brown sugar in a medium bowl. Arrange evenly in an 8 or 9 inch square baking pan. In another medium bowl, combine the oats, flour, and spices to mix. Cut in the butter until the mixture is crumbly and forms pea size little lumps. Gently mix in the cheese. Sprinkle this mixture evenly over the apples and bake for 35 to 40 minutes until the juices bubble up and the top is nicely browned. Let rest for 10 minutes and serve with heavy cream.