Bring a large pot of salted water to boil. Add the rice and barley and cook until al dente, 15 minutes. Drain well.
Heat the oil in a large skillet over medium heat. Add the onion, garlic, pepper flakes (if using) and salt and pepper to taste. Cook until the onion is tender and beginning to brown, 5 minutes. Stir in the drained rice mixture. Add 2 cups broth, cover and cook until the rice and barley are tender, 6 to 8 minutes.
Stir in the asparagus and mushrooms and continue to cook, covered, until the vegetables are tender, 8 to 10 minutes. Remove from the heat and stir in the remaining 1/2 cup broth, cream cheese and Parmesan until melted and creamy. Sprinkle with chives and zest.