Combine the 1/2 cup basil, freshly minced garlic cloves, olive oil, lemon juice, red wine vinegar, sugar, salt, and red pepper flakes in a blender. Blend for 2 minutes until the basil is fully incorporated and the dressing is smooth and vibrant green. I always use fresh basil and garlic for this step because they make a noticeably brighter, more aromatic dressing than dried alternatives. Transfer to a bowl and set aside while you prepare the other components.
Bring a large pot of salted water to a rolling boil and add the pasta. Cook for 7 to 8 minutes until al dente—you want the pasta to have a slight firmness in the center because it will continue to absorb the dressing as it cools. Drain the pasta into a colander and rinse thoroughly with cold water for about 1 minute to stop the cooking process and remove excess starch, which helps prevent the pasta from becoming mushy.
While the pasta cooks, halve the tomatoes lengthwise and set aside. Finely dice the red onion into 1/4-inch pieces for even distribution throughout the salad. Gently pat the mozzarella balls dry with paper towels—this is crucial because excess moisture will dilute the dressing and make the salad watery. Roughly chop the 1/3 cup fresh basil for garnish and have the toasted pine nuts ready.
Transfer the cooled pasta from Step 2 to a large mixing bowl. Pour the basil vinaigrette from Step 1 over the warm pasta and toss gently to coat evenly—the warm pasta will absorb the dressing better than cold pasta. Add the halved tomatoes, diced red onion from Step 3, and the mozzarella balls. Gently fold everything together to combine, being careful not to break the mozzarella. I like to let the salad sit for 5-10 minutes before serving so the flavors meld together beautifully.
Transfer the pasta salad to a serving bowl or platter. Top with the fresh basil and toasted pine nuts for color and crunch. Drizzle with balsamic glaze just before serving for a subtle sweet-tart finishing touch. Serve immediately at room temperature, or cover and refrigerate for up to 2 hours if you prefer it chilled.