Make the vinaigrette:
Put the basil, olive oil, Parmigiano, vinegar, lemon juice, garlic, and lemon zest in a blender. Blend until smooth. Season with salt and pepper to taste
Make the salad:
Put 4 to 6 quarts of salted water in a large pot and bring to a boil over high heat.
Drop the green beans and/or wax beans into the boiling water and cook until the beans are just crisp-tender, about 4 to 5 minutes. Remove the beans from the water with a slotted spoon, and transfer to a baking sheet lined with paper towels to drain and cool. Drop the peas in the water and cook until just tender, about 2 to 3 minutes for fresh peas (frozen peas only need a minute or so to thaw them). Remove the peas from the water with a slotted spoon and transfer to the paper towel-lined baking sheet to drain. Gently blot the peas and beans dry.
Return the water to a boil and add the pasta. Cook just until al dente, following package instructions. Drain the pasta thoroughly by shaking it in a colander and immediately pouring it out onto a rimmed baking sheet. Toss the pasta with the olive oil to prevent sticking.
Transfer the cooled pasta to a large serving bowl. Add the beans, peas, and cherry tomatoes and toss. Add just enough vinaigrette to moisten the pasta, taking care not to overdress it (you may not need it all). Add the pine nuts and toss again. Let the salad rest for 10 to 15 minutes to allow the flavors to meld and then taste the salad again. If necessary, add a little viniagrette and salt and pepper. Serve as soon as possible.