Drain artichokes over a bowl, reserving 3 tablespoons marinade. Chop artichokes, and combine with 1 tablespoon reserved marinade, pimento, and 1/2 teaspoon rosemary; set aside.
Combine 2 tablespoons reserved marinade, 1/2 teaspoon rosemary, and garlic in a small bowl; brush over fish, and sprinkle with pepper.
Place a grill pan coated with cooking spray over medium-high heat. Add fish; cook for 2 minutes on each side until the fish is medium-rare (or desired degree of doneness); keep warm.
Place rolls, cut sides up, on a baking sheet; broil for 2 minutes or until toasted. Spread mayonnaise evenly over bottom halves of rolls. Top each roll half with a tuna steak and 1/4 cup artichoke mixture; cover with roll tops.