Cook the pasta in generously salted water 1 minute past al dente, about 12 minutes. Drain and rinse under cold water until fully cool, then shake off the excess.
Whisk the pesto, mayonnaise, lemon juice, olive oil, salt, and pepper together until smooth and creamy. The lemon juice is what keeps the pesto bright green — don't leave it out.
Set aside about 1/4 cup of the dressing for later. Pour the rest over the cooled pasta and toss until every piece is coated.
Fold in the cherry tomatoes, mozzarella pearls, and most of the torn basil.
Chill for at least 30 minutes. Before serving, stir in the reserved dressing to loosen it, then top with the remaining basil and toasted pine nuts.