Lay the slices of bacon on a wire rack set over a baking sheet. Cook until crisp, 15 to 20 minutes. Set aside until cool enough to handle while you prepare the pasta.
Bring a large pot of salted water to a boil.
Shave the zucchini into thin ribbons with a vegetable peeler or mandolin. (Or slice into a thin julienne with a knife.) Place the ribbons of zucchini in a large bowl and season lightly with salt and a few grinds of freshly ground black pepper. Add the grated cheese and toss to combine. Crumble the bacon into the bowl.
Cook the pasta until just tender, 8 to 10 minutes. Drain the pasta, reserving about 1/4 cup of the pasta water. Immediately transfer the pasta to the bowl with the zucchini along with the reserved pasta water. Mix well and add the basil. Season with salt and pepper.
Divide the pasta among the plates and top with more cheese.
Adding some of the pasta water brings out the full flavor of the pasta.