In a medium bowl, toss the zucchini with the flour and a pinch of salt. In a very large skillet, heat half of the oil until shimmering. Add half of the zucchini and fry over high heat, turning once or twice, until browned and crisp, 3 to 4 minutes. Using a slotted spoon, transfer the zucchini to a paper towellined wire rack and season with salt. Repeat with the remaining oil and zucchini.
Meanwhile, cook the spaghetti in a large pot of boiling salted water until al dente. Drain, reserving 1/2 cup of the pasta cooking liquid. Return the pasta to the pot and toss with the 1 cup of cheese, the basil and a generous pinch of pepper. Add the reserved pasta water a little at a time, tossing well to coat. Transfer the pasta to a bowl and top with the crispy zucchini. Serve right away with lemon wedges and additional cheese.