2 cups (packed) fresh basil leaves
½ cup (packed) fresh mint leaves
½ cup lightly toasted pistachios or pine nuts
2 large cloves garlic, grated or pasted
1 jalapeño, seeded and coarsely chopped
1 tsp. crushed red pepper
Juice of 1 small lime or lemon or a splash of white wine vinegar
¾ cup grated Pecorino Romano
¾ cup grated Parmigiano-Reggiano
⅓ cup EVOO
1 tbsp. EVOO
2 tbsp. butter
1 firm medium zucchini—halved, seeded, then cut into 1/4- to 1/2-inch pieces
2 ears corn, husked, kernels removed
1 leek, split lengthwise, whites and light greens thinly sliced
Salt and pepper
1 lb. spaghetti or tagliatelle
Bring a large pot of salted water to a boil over high. Prepare an ice bath. Add the basil to the boiling water and cook for 15 seconds. Using a spider or a slotted spoon, transfer the basil to the ice bath, then transfer to a kitchen towel to drain.
In a food processor, pulse the basil, mint, nuts, garlic, jalapeño, crushed red pepper, and lime juice until a thick paste forms. Add the cheeses; pulse a few times. With the machine running, slowly stream in the EVOO. Mix until the pesto is almost smooth.
Bring the large pot of water back to a boil. Heat a large skillet over medium. Add the EVOO, one turn of the pan. Melt the butter into the oil. Add the zucchini, corn, and leek; season with salt and pepper. Cook until the leek softens, 5 to 6 minutes.
Add the pasta to the boiling water and cook for 1 to 2 minutes less than the package directions. Scoop out about 3/4 cup cooking water, then drain the pasta. Add the pasta and the pesto to the skillet with the vegetables. Toss, adding pasta water as needed to coat the pasta in the pesto.