Cook the linguine in a large pot of boiling salted water until al dente. Reserve 1/4 c. of the pasta cooking water then drain the pasta. Meanwhile, in a food processor, puree the dill, basil, garlic and 3 T. olive oil. In a large deep skillet, heat the remaining 3 T. of olive oil. Add the green onions and cook over low heat, stirring occasionally, until softened, about 10 minutes. Spread the zucchini on top of the green onions, cover and cook about 6 minutes. Add the pasta to the skillet along with the reserved pasta cooking water. Add the herb puree, cheese, salt and pepper and toss well. Serve.