Bring a large pot of salted water to a boil. While you’re waiting, in a medium saucepan or skillet, heat sunflower oil over medium-high heat. Fry zucchini slices in batches for about 3 to 4 minutes, flipping once, until golden on both sides. [Update to add: If your zucchini isn’t browning right away, bump up the heat until it does in just a few minutes.] Drain in colander, shaking with a couple pinches of salt, then transfer to a large bowl and pour vinegar on top. Set aside. In the hot water, cook edamame for 3 minutes, frozen peas for 3 to 4 minutes, or fresh peas for 1 to 2 minutes (to taste). Drain and run cool water over until lukewarm. Set aside to dry. Leave pot boiling, then cook pasta until al dente in it. Drain and rinse under cold water. Combine half of basil and all of the parsley and olive oil in a food processor or blender. Blend until smooth, then season with salt and pepper. Transfer pasta back to empty pot. Add fried zucchini and any juices, basil-parsley oil, edamame or peas, lemon zest, capers and mozzarella. Stir gently together, then season generously with salt and pepper. Right before you serve it, stir in remaining basil leaves.