In microwave oven heat butter and oil in a 14 by 11 by 2-inch dish, uncovered, at 100 percent for 3 minutes. Add scallion whites, celery, parsley, and rice and stir to coat. Cook, uncovered, at 100 percent for 4 minutes.
Stir in broth and cook, uncovered, at 100 percent for 12 minutes. Add asparagus, shrimp, and peas and stir well. Cook, uncovered, for 12 minutes more.
Remove from oven. Stir in salt and pepper. Cover loosely with paper toweling and let stand for 8 to 10 minutes. Uncover, sprinkle with scallion greens and cheese, and serve.