Bring a large pot of water to a boil and salt it. Halve the zucchini and scrape away the seeds from the centers. Boil the zucchini for 5 minutes, then, using tongs, transfer to paper towels to drain. Leave the water at a low boil. Coarsely chop the zucchini.
In a small skillet, toast the nuts over medium heat until golden and fragrant. Place half of the nuts in a food processor and let cool; reserve the remaining nuts.
Add the zucchini to the food processor along with the mint, parsley, garlic and lemon juice; season with salt and pepper. Add the cheese and process. With the machine on, stream in the EVOO until the pesto is just turning from finely chopped to saucy. Transfer to a large, shallow serving bowl.
Bring the reserved water to a rolling boil, add the pasta and cook until al dente. Add about 1/2 cup of the pasta cooking water to the pesto. Drain the pasta and toss with the sauce for 1 to 2 minutes to combine. Top with the reserved toasted nuts.