Start by finely chopping the cabbage and grating the carrots with a box grater.
Heat olive oil in a large pan or cast-iron skillet over medium heat and cook the cabbage and carrots until they soften, about 5 to 6 minutes.
While the vegetables cook, beat the eggs in a large bowl and mix in the sea salt, black pepper, red pepper flakes, and soy sauce.
Add chopped parsley, sliced green onions, and grated mozzarella cheese to the egg mixture and stir well.
Pour the egg mixture evenly over the cooked cabbage and carrots in the skillet, then cover the pan with a lid.
Let it cook on medium-low heat until the edges start to pull away and only small wet spots remain on the surface, approximately 5 to 6 minutes.
Carefully transfer the omelette onto a plate, flip the plate and skillet together, and slide the omelette back into the pan to cook the other side until golden brown, about 3 to 4 minutes.
Serve the omelette right away, garnished with extra parsley and a sprinkle of roasted sesame seeds if you like.