1. Place butter, oil and onion in a large, microwave-safe bowl. Microwave, uncovered on high, until butter melts and onion begins to soften, about 3 minutes. Stir in rice, and microwave, uncovered on high, until rice begins to turn translucent, about 3 minutes.
2. Stir in broth, cover with microwave-safe plastic wrap or use a lid, and microwave on high until mixture is at a full boil, 10 to 14 minutes.
3. Meanwhile, chop ham if necessary, and set aside. Rinse and snap tough ends off asparagus, and chop into 1/4-inch rounds. Set aside.
4. Remove the bowl from microwave, uncover, and stir well. Continue to microwave on high, uncovered, for 10 more minutes or until rice is almost done. Rice will be very moist and al dente in texture, but not soupy.
5. Stir in ham and asparagus, and continue to microwave, uncovered, until rice is done and asparagus is crisp-tender, about 2 to 3 minutes. Stir in cheese, salt and pepper to taste, and serve immediately. Serve additional cheese for topping at the table, if desired.
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