Cook the pasta: Bring a large pot of salted water to a rolling boil. Add farfalle and cook until al dente (check the package and subtract 1 minute). Reserve 1/2 cup pasta water, then drain and spread on a tray to cool slightly.

Toast the nuts (optional): In a dry skillet over medium heat, toast pine nuts or almonds for 3–4 minutes, stirring, until fragrant and lightly golden. Set aside to cool.

Prep the vegetables: Halve the tomatoes, dice the cucumber, thinly slice the red onion, and slice the olives. Pat the mozzarella dry if needed.

Loosen the pesto: In a large mixing bowl, stir pesto with 1 tablespoon lemon juice and 1–2 tablespoons of the reserved pasta water until glossy and pourable. Add a splash of olive oil if it still seems thick.

Toss the pasta: Add warm (not hot) farfalle to the bowl and fold to coat every piece. The slight warmth helps the pesto cling.

Add mix-ins: Gently fold in tomatoes, cucumber, red onion, olives, mozzarella, and Parmesan. Add lemon zest and more lemon juice to taste.

Season: Taste and season with salt and black pepper. Add more olive oil or a spoonful of pasta water if you want a looser salad.

Finish and chill: Sprinkle with toasted nuts and torn basil. You can serve right away, or chill for 30–60 minutes to let flavors mingle.

Before serving: If chilled, refresh with a drizzle of olive oil and a squeeze of lemon. Top with extra Parmesan.