1. In a medium-size bowl, whisk together eggs, milk, mustard, salt, cayenne and nutmeg.
2. In a large bowl, toss apples, bread cubes and bacon together. Coat 13 x 9 x 2-inch baking dish with nonstick cooking spray. Arrange bread mixture in baking dish. Pour egg mixture evenly over the top. Gently press bread mixture with a wooden spoon to ensure all the bread is moistened. Top with shredded cheese. Cover with nonstick foil and refrigerate overnight.
3. To bake, heat oven to 400 degrees F. Remove strata from refrigerator and bake, covered, at 400 degrees F for 30 minutes. Remove foil and bake for 10 more minutes, until top is nicely browned. Let stand 10 minutes before serving.