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