In a small bowl, mix olive oil, 1 tbsp balsamic vinegar, lemon zest, shallot and garlic. Set aside.
Bring a pot of water large enough to cook pasta to a boil. Blanch snap peas 1-2 minutes and remove to colander (keep boiling water on stove). Rinse peas under cold water until cool. Set aside
Cook pasta in reserved boiling water according to package directions. Drain, do not rinse, and transfer to a large, shallow bowl. Add olive oil mixture to hot pasta and mix well to combine. Allow pasta to cool to room temperature.
When pasta has cooled, add peas, snap peas, mozzarella, spinach, scallions and mint. Toss well. Drizzle remaining 2 tbsp balsamic vinegar and mix well. Salt and pepper to taste, serve at room temperature.