Rinse the Brussels sprouts with cool water. Trim the stalk off the sprouts, and remove any damaged or brown leaves.
Slice each sprout into quarters, and place on a cookie sheet. Pat the sprouts dry, Add the diced apples.
Drizzle with olive oil and sprinkle with salt and pepper. Use your hands to make sure everything is coated evenly with oil.
Roast the Brussels sprouts:
Bake at 400 degrees F for about 40 minutes until the Brussels sprouts are soft inside and browned and crisp outside. Stir the sprouts every 15 minutes to make sure they cook evenly.
Notes
These are best eaten right away, but you can store leftovers in the refrigerator for up to 3 days.