Preheat the oven to 350 degrees F. Scatter the pecans on a rimmed sheet pan and toast until they are fragrant and a shade or two darker, 7 to 8 minutes. Cool.
Bring a large pot of salted water to a boil. Add the pasta to the boiling water and cook according to the package directions until al dente. Drain, reserving about 1/2 cup pasta water.
Meanwhile, put the pecans in a food processor with the lemon zest, basil, parsley and garlic and pulse six or seven times to make a chunky paste. Scrape down the sides of the work bowl and, with the processor running, add the olive oil in a steady stream to make an almost-smooth pesto.
Scrape the pesto into a large serving bowl and stir in the cheese. Season with salt. Add the spaghetti and toss, adding the reserved pasta water to loosen, if needed.