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 into the mixture, cover, and marinate in the refrigerator 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 the artichoke and marinade mixture, and toss to coat.