Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain and return to the pot, reserving 1 cup of the pasta cooking water.
While the pasta is working, using a food processor, finely chop the cheese, parsley, mint, chiles, garlic, pistachios, lime zest and lime juice; season with salt and pepper. With the machine on, stream in about 5 tbsp. EVOO to form a pesto.
In a large skillet, heat about 1 tbsp. EVOO over medium- high heat. Add the butter and heat until foaming. Add the zucchini and cook, stirring, until lightly golden, about 10 minutes; season with salt and pepper.
Add the pesto and reserved pasta cooking water to the pasta and toss, 1 to 2 minutes. Stir in half of the zucchini. Serve the pasta in shallow bowls and top with the remaining zucchini.