Cook the pasta al dente according to package directions. Drain and immediately toss with the baby spinach until the spinach wilts. Rinse under cool water to speed cooling, or let sit for 15-20 minutes until room temperature.

In a large bowl, combine the cooled pasta and spinach with the julienned sun-dried tomatoes, halved cherry tomatoes, sliced red onion, shredded Parmesan, mozzarella pearls, and chopped basil. If the pasta is still warm, wait to add the mozzarella until it has cooled to avoid melting.

In a small bowl, whisk together all dressing ingredients. Pour about 3/4 of the dressing over the pasta salad and toss to coat. Reserve the remaining 1/4 of the dressing for later. Cover and refrigerate for at least 30 minutes. Before serving, let the salad sit at room temperature for about 15 minutes, then toss with the reserved dressing.