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Heat oil and butter in a saute pan over medium heat. Add the orzo and stir until browned, about 1 minute.
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Add carrots, salt, and pepper, stir for another minute.
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Add the rice and saute, stirring, until rice is coated with oil and butter.
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Add the broth and bring to a boil. Reduce the heat to low and cook, covered, for 15 minutes.
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Remove from heat and add the zucchini, then let stand covered for 5 minutes.
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Stir in parsley before serving.