Place the red cabbage in a microwave-safe bowl with 1/3 cup water. Microwave for a couple of minutes until the water turns purple.
Separate the egg into 2 small bowls. Add 2 tablespoons of the purple water to the egg white, whisking vigorously to combine for a uniform color.
Heat a little oil to coat the bottom of a small nonstick skillet over medium heat. Add the green egg white and top with the egg yolk (so it resembles a fried egg). Cook until the white (green) is set. Plate and enjoy!