Bring a large pot of water to a boil; add 1 teaspoon salt. Add peas, and cook until tender, 3 to 4 minutes for fresh peas and 1 minute for frozen. Using a slotted spoon, transfer peas to a medium bowl; set aside. Add zucchini to pot, and cook 30 seconds; using a slotted spoon, transfer to bowl with peas.
Put yogurt and basil into a large, heatproof bowl; season with salt and pepper. Set bowl over the boiling water, and whisk until mixture is warm, about 1 minute. Remove from heat. Add peas and zucchini to bowl; set aside.
Cook pasta in salted boiling water until al dente; drain. Add pasta to vegetables and sauce, and toss to combine. Season with salt and pepper. Serve topped with cheese.