Bring water for the pasta to a boil, then add salt. Once boiling again, add spagettini and cook for about 5 minutes or 1 minute less than given on package. Reserve 1 cup of the pasta cooking liquid and drain.
While the pasta is cooking, heat the olive oil in a wide sauté pan or wok. Add the sliced garlic and fry gently over medium-high heat until it starts to color. Add the zucchini and sauté until they start to soften and color.
Add the tomato sauce. If the pan looks a little dry, add water from the pasta pot to it, ¼ cup at a time.
Just before the pasta is done, add the grated cheese to the zucchini. Mix well and cook for a minute. Taste for salt.
Add the basil to the sauce, stir to mix, then add the pasta. Toss together and cook for 1 minute more, adding the reserved water if needed. It''s ready! Serve with extra cheese if desired.
Tear delicate basil leaves into pieces instead of chopping them to bring out the oils. If you are in chemo, add them in step 4.