Bring a large pot of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain.
Heat olive oil in a skillet over medium heat. Stir in the onions, green onions, and pesto. Cook until tender. Mix in salmon, and cook until heated through. Stir in 1/2 the Parmesan cheese, and continue cooking 5 minutes. Toss with the cooked pasta, and sprinkle with remaining Parmesan cheese to serve.