For the pasta: Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, 8 to 10 minutes. Drain and place in a serving bowl. Add the cheese and toss until coated.
For the sauce: In a small saucepan, bring the olive oil, lemon juice, lemon zest, and garlic to a simmer over medium-low heat. Cook for 5 minutes. Remove the pan from the heat and stir in the mint and parsley.
Pour the sauce over the cooked orzo, toss until coated, and season with salt and pepper, to taste.