Bring a large pot of water to a boil for the pasta.
In a large skillet with a lid, heat 1 tbsp. olive oil, one turn of the pan, over medium-high. Add the zucchini and season with salt and pepper. Cook, stirring occasionally, until lightly browned and crisp-tender, 6 to 7 minutes. Transfer to a plate. Add the remaining 2 tbsp. olive oil, two turns of the pan; add the garlic and chile and swirl until aromatic, about 1 minute. Add the tomatoes and basil and season with salt. Cover and cook, shaking the pan occasionally, until the tomatoes break down into a sauce, 10 to 12 minutes.
Salt the boiling water, add the pasta and cook until almost al dente. Reserve 1/2 cup of the starchy cooking water; drain the pasta. Toss the pasta and cooking water with the sauce; drizzle with EVOO. Fold in the zucchini and season. Serve in shallow bowls topped with the mint and ricotta salata.