Place pita rounds on a large baking sheet. Place one-fourth of artichoke, tomato, basil, and dressing down center of each pita. Sprinkle each serving with 1/4 cup cheese. Broil 3 inches from heat (with electric oven door partially opened) 2 to 3 minutes or until cheese melts.
Remove from oven. Roll up each pita; wrap bottom of each pita roll in wax paper or decorative tissue paper, and serve immediately.