Add mayonnaise, vinegar, lemon juice, sugar, salt, pepper, Italian seasoning, garlic, and parmesan to a food processor. Run the food processor until all the ingredients are fully combined and garlic is fully minced, then drizzle the oil in slowly.
Combine the lettuce, olives, pepperoncini, onion, and tomatoes in a large mixing bowl. Pour half of the dressing on top and then toss to coat. Add the rest of the dressing and toss to coat again, so everything is equally coated. Top with croutons and give one last toss. Set in the fridge for 5 minutes to let all the flavors meld together.