Bring 3 litres of water to a rolling boil and add the salt. Cook the pasta according to package instructions, plus one additional minute. Drain using a colander, rinse thoroughly under cold water, and shake off any excess moisture. Allow the pasta to fully cool and dry.
To prepare the pesto, combine basil leaves, parmesan, toasted pinenuts, garlic, salt, pepper, and olive oil in a narrow container suitable for an immersion blender. Blend until mostly smooth—aim for a textured consistency with small green flecks rather than a completely uniform puree.
Transfer the cooled pasta into a large mixing bowl. Spoon in the prepared pesto and add the mayonnaise. Toss thoroughly to coat all the pasta. Gently mix in the halved bocconcini and cherry tomatoes, stirring just enough to distribute evenly. Add the arugula and lightly fold through to incorporate.
Transfer the salad to a serving dish and scatter with fresh basil leaves if using. Serve at room temperature for best flavor and texture.