In a medium container with a lid, mix canola oil, tarragon vinegar, sugar, thyme, dry mustard, and garlic. Cover, and shake until well blended. Place artichoke hearts in mixture, cover, and marinate in the refrigerator, at least 4 hours or overnight.
In a large bowl, toss together lettuce, red bell pepper, carrot, red onion, black olives, green olives, cucumber, and Romano cheese. Season with pepper. Pour in artichoke and marinade mixture; toss to coat.
