Melt coconut oil in a small skillet over medium heat.
Beat egg and egg white together in a small bowl.
Cook and stir egg mixture in hot coconut oil until just starting to set, about 30 seconds. Stir sun-dried tomatoes, yellow onion, green onion, and Cheddar cheese into egg mixture; cook and stir until eggs are almost completely set; 2 to 4 minutes. Add spinach to eggs; cook and stir until spinach wilts. Transfer eggs to a plate and top with avocado.