In a large skillet, melt the butter over medium heat. Add the oil, carrots, celery, cauliflower, broccoli, ham and onion. Cover and cook for 15-20 minutes or until vegetables are crisp-tender, stirring occasionally.
Stir in the rice; cook until heated through. Sprinkle with cheese. Remove from the heat; cover for 2 minutes or until cheese is melted.