Combine the basil, Parmesan, pine nuts, garlic, lemon juice, salt, and pepper in a food processor. Pulse several times to break everything down. With the processor running, slowly drizzle in the olive oil through the feed tube until you reach a smooth, thick sauce. Taste and adjust salt and lemon. Set aside.

Bring a large pot of generously salted water to a rolling boil. Cook pasta according to package directions until al dente — you want a slight bite, not mush. Before draining, scoop out about ¾ cup of pasta water and set it aside. Drain the pasta, then rinse thoroughly under cold running water until completely cool. Drain well.

Transfer the cooled, well-drained pasta to a large mixing bowl. Pour all of the pesto over the pasta and toss vigorously until every piece is coated. If the pesto feels thick or the pasta seems dry, add a small splash (2–3 tablespoons) of the reserved pasta water and toss again. The pasta should look glossy and lightly sauced — not swimming in pesto and not dry.

Add the cherry tomatoes, sun-dried tomatoes, Kalamata olives, and half the toasted pine nuts. Toss gently to combine. Add the fresh mozzarella and arugula last, folding them in carefully so the cheese stays intact and the arugula doesn’t wilt. Drizzle with the lemon juice and season generously with salt, pepper, and red pepper flakes.

Taste and adjust seasoning one final time. Transfer to a large, beautiful serving bowl. Scatter the remaining pine nuts and a generous handful of freshly grated Parmesan over the top. Garnish with fresh basil leaves. Serve immediately at room temperature, or refrigerate for 30 minutes for a colder, slightly more melded flavor profile.