Cook the pasta: Boil in salted water until al dente. Drain, then toss with 1 tablespoon olive oil to prevent sticking. Let cool for 10 minutes.
Make the dressing: In a large bowl, stir together Greek yogurt, pesto, lemon zest, and 1–2 tablespoons lemon juice.
Add Parmesan. Season with salt, pepper, and a pinch of red pepper flakes if you like heat.
Add chicken and veggies: Fold in the cooked chicken, tomatoes, cucumber, spinach or arugula, and red onion.
Combine with pasta: Add the cooled pasta to the bowl. Toss until everything is well coated.
If it seems thick, loosen with a splash of water or a drizzle of olive oil.
Taste and adjust: Add more lemon, salt, or pepper as needed. The flavors should be bright, creamy, and well seasoned.
Finish and serve: Sprinkle with toasted nuts for crunch. Serve right away, or chill for 30 minutes for a colder salad.