Bring a large pot of water to a boil for the pasta.
Heat about 2 tablespoons EVOO, two turns of the pan, in large skillet over medium heat. Add the zucchini to the hot EVOO and lightly brown, 6-8 minutes. Add the spring onions and half the garlic; deglaze with wine and season with salt and pepper. Reduce the heat and keep warm until the pasta is done.
Meanwhile, place the mint, parsley, remaining garlic, nuts, cheeses, lemon zest and lemon juice and about 1/4 cup EVOO in a food processor. Pulse into a pesto and season with salt and pepper, to taste. Transfer the pesto to a large bowl.
Salt the pasta water and cook the tagliatelle to al dente. Add 1 cup of the starchy cooking water to the pesto. Drain the pasta and add it to the the bowl. Toss to combine, then add the zucchini and gently toss. Serve.