Heat 1/2 teaspoon coconut oil in a small skillet over medium heat. Whisk together one egg and one egg white; add to skillet and tilt until bottom is coated. Push cooked eggs toward the center of the skillet and tilt again to allow uncooked eggs to coat the bottom. Continue for 1-2 minutes or until eggs are no longer runny but still appear wet.
Sprinkle a small amount of onions, 1 cup of spinach and 1 1/2 tablespoons shredded Parmesan in center of omelet and fold one side toward the center. Fold other side toward the center; remove from heat. Repeat with remaining ingredients until 4 omelets have been cooked.
Serve each omelet warm with 1/2 cup cherries on the side.