Heat the oil in a large pot or a pan over high heat. Add the mushrooms, don't stir for the first 2 minutes letting the mushrooms brown. Start stirring, and cook the mushrooms for 2-3 minutes.
2 tablespoons frying oil
Reduce the heat to medium-low, add butter, shallots, and cook for 1-2 minutes. Add garlic and thyme and cook for another minute.
Add orzo and broth, bring to a boil, and simmer for 8 minutes or until orzo is cooked through and al dente (soft but still has a bite to it). It may look too runny at first but it will thicken further while cooling. Cooking time may vary depending on the brand of the orzo!