Cook the pasta. Bring a large pot of salted water to a boil. Cook the pasta until just al dente. You want a little bite so it holds up in the salad.
Cool it down. Drain the pasta and rinse under cool water to stop the cooking.
Shake off excess water. Toss with a drizzle of olive oil so it doesn’t stick.
Toast the nuts. In a dry skillet over medium heat, toast pine nuts until lightly golden and fragrant, 2–3 minutes. Keep them moving so they don’t burn.
Make the pesto. In a food processor, add basil, garlic, toasted nuts, Parmesan, lemon zest, and a pinch of salt and pepper.
Pulse to break it down. With the motor running, stream in olive oil until the pesto is smooth but still a little textured. Stir in a squeeze of lemon juice.
Taste and adjust salt, pepper, and lemon.
Prep the veggies. Halve the tomatoes, dice the cucumber, and slice the onion or shallot thin. If using arugula, keep it dry so it stays perky.
Toss it together. In a large bowl, combine cooled pasta, tomatoes, cucumber, onion, arugula, and mozzarella. Add several spoonfuls of pesto and toss gently to coat.
Add more pesto until every piece has a glossy green hug.
Season and brighten. Add a pinch of salt, a few grinds of black pepper, and another squeeze of lemon if needed. If it feels thick, loosen with a tablespoon or two of pasta water or a drizzle of olive oil.
Finish and serve. Top with extra Parmesan, a few toasted nuts, and a crack of pepper. Serve chilled or at room temperature.