Use a knife or a mandolin to slice the cabbage as thin as you can get it, so it is almost shaved. Do the same with the red onion. Combine the cabbage, red onion, and carrots in a large bowl.
In a small bowl, combine the olive oil, red wine vinegar, Italian seasoning, salt, and pepper. Use a small whisk to blend the dressing.
Toss the dressing with the salad ingredients and top with fresh parsley if desired.