Cook the pasta: Bring a large pot of salted water to a boil.
Cook the pasta until just al dente. Drain well and spread on a sheet pan to cool slightly, then drizzle with a bit of olive oil to prevent sticking.
Prep the chicken: If using rotisserie, remove skin and bones, then shred or cube. For grilled or poached chicken, season lightly and let it cool before dicing.
You want bite-size pieces.
Chop the veggies: Halve the tomatoes, dice the cucumber, slice the onion, and slice the roasted red peppers and olives. Keep everything roughly the same size for easy eating.
Make the dressing base: In a large bowl, whisk the pesto with lemon zest and juice. Add 1–2 tablespoons of olive oil to loosen it.
Taste and season with salt and pepper.
Toss the pasta: Add the slightly warm pasta to the bowl and toss to coat. Warm pasta absorbs flavor better, so don’t chill it completely first.
Add chicken and mix-ins: Fold in the chicken, tomatoes, cucumber, onion, roasted red peppers, olives, and mozzarella. Sprinkle in the Parmesan and toss again until everything is evenly coated.
Adjust and brighten: If it looks dry, add another spoonful of pesto or a drizzle of olive oil.
Squeeze a bit more lemon if needed. Season with more salt and pepper to taste.
Finish and serve: Top with toasted pine nuts and torn basil. Serve right away slightly warm, or chill for at least 30 minutes for a colder salad with melded flavors.