Cut 3 of the zucchini into fine strips, about 3 inches long by ¼ inch. Chop the fourth very finely in a food processor. Slice the onion in half from root to stem end, then cut into fine strips in the same direction.
Heath the oil in a large skillet over medium-high heat. Fry the zucchini strips until a few are just beginning to brown, about 5 minutes. Add the onion and fry another 3 or 4 minutes, until the onion is wilted but sill a little bit crunchy.
Add the grated zucchini and toss well with the already fried vegetables. Toss in the parsley. Fry only 1 minute, seasoning with salt and pepper. Transfer the vegetables to a large serving bowl.
Cook the pasta in at least 4 quarts of boiling water with 2 tablespoons of salt. Drain well and pour the pasta into the bowl with the vegetables. Add the ricotta and toss well.
Serve immediately, passing grated cheese at the table.