Combine olive oil, mayonnaise, vinegar, lemon juice, sugar, salt, pepper, Italian seasoning, garlic, and Parmesan in a food processor, and process until thoroughly combined.
Combine salad mix (cos and iceberg, shredded red cabbage, shredded carrots, sliced radish), olives, pepperoncini, onion, tomatoes, and croutons in a large bowl. Drizzle salad with dressing; toss to coat. Let stand for 5 minutes before serving.
