Heat the olive oil in a large skillet over medium heat. Add the finely chopped onion and cook for 2-3 minutes until softened.
Stir in the grated carrot and shredded cabbage. Continue sautéing for 8-10 minutes, stirring occasionally, until the cabbage is tender but slightly crisp.
In a separate bowl, beat the eggs. If you prefer a thicker texture, whisk in the optional tablespoon of flour. Add the beaten eggs to the skillet, stirring gently to combine with the cabbage and carrots. Cook for 2-3 minutes, allowing the eggs to scramble and cook through.
If desired, sprinkle grated Manchego cheese over the top of the dish and let it melt into the eggs and cabbage.
Garnish with freshly chopped parsley and serve hot.