Bring a large pot of salted water to the boil and then add the linguine. While the pasta is cooking, pour the olive oil into a large frying pan and throw in some peeled cloves of garlic. Cook over gentle heat until the garlic starts to turn light brown and its scent wafts upward. Remove the cloves from the pan and take the pan off the heat. Roughly chop or shred a mound of basil leaves, set aside. In a second dry frying pan, toast a handful or so of pine nuts. When the pasta is ready, drain it, toss it in the garlic-infused olive oil, and then transfer to a warm bowl. Grate over some Parmesan, then, using a vegetable peeler, shave in some pecorino and sprinkle with the toasted pine nuts. Toss well, throw over all but a small handful of the basil leaves, and turn again. Grate a little more cheese over and sprinkle with the remaining shredded basil leaves.