The shape of orecchiette pasta is perfect for holding the savory sauce made from the mushrooms as they cook. If you have any leftovers, serve them at room temperature the next day.
Bring a large pot of water to a boil. Add pasta and cook until al dente, about 10 minutes; reserve ½ cup of the cooking water and then drain well. Transfer pasta to a large bowl.
Meanwhile, heat oil in a large skillet over medium-high heat. Add onion, cook for 1 minute, then add mushrooms and cook until tender, 4 to 5 minutes. Add peas and cook until just tender, about 2 minutes more.
Transfer vegetables, green onions, cheese, salt, and pepper to bowl with pasta and toss well, adding some of the reserved pasta water, if needed, for moisture. Serve hot.