Heat the butter and the oil in a microwave-safe, 3-quart casserole dish, uncovered, for 2 minutes. Add the shallots and cook, uncovered, for 2 minutes. Add the rice and stir to coat with the oil. Cook for 2-1/2 minutes.
Add the broth, dried mushroom, and vermouth and cook uncovered for 11 minutes. Stir well and cook 6 minutes more. Mix in the asparagus and thyme and cook for 5 minutes.
Remove from the microwave and let stand, uncovered, for 5 minutes. Stir in the cheese and chives, add salt and pepper as desired, and serve immediately.
To make ahead for a party, prepare through cooking with the broth and set aside. When you are ready to serve diner, add the asparagus and thyme and finish preparation from there. Serve immediately.