In a large pan, cook the pasta in boiling salted water according to pkg directions. I add about 1 tbl olive oil to my pasta water too.
As soon as you put the pasta water on to boil, heat 3 tbl olive oil in a heavy saucepan over low heat. Gently saute the whole garlic cloves until each clove is just golden brown and easily pieced with a fork. Remove garlic cloves and on a cutting board mash cloves with a fork and mix with anchovy paste. Turn burner off.
As soon your pasta water begins to boil and you've added the pasta, reheat the sauce pan of oil. Return mashed garlic/anchovy paste to the warm olive oil and simmer for a minute. Add basil and green onions, gently stir, making sure the mashed garlic is distributed and simmer for about 1-2 minutes. Add cream, Parmesan cheese, parsley and salt and pepper to taste. Add shrimp and simmer for less then a minute. Toss shrimp and sauce with drained pasta and serve.