Bring a large pot of salted water to a boil. Cook pasta to al dente according to package directions. Drain and immediately rinse with cold water to stop the pasta from cooking.
In a large bowl, toss pasta with olive oil. Gently stir in strawberries, mozzarella cheese, red onions and basil. Pour half of the pasta onto a serving platter or bowl, and drizzle with balsamic glaze. Then pour the remaining half of the pasta salad on top, and drizzle with more balsamic glaze. Garnish with extra basil if desired.
BALSAMIC GLAZE: In a small saucepan, whisk together balsamic vinegar and sugar. Bring to a boil over medium high heat, then reduce heat to medium low and simmer for 10 minutes or until reduced by half. Allow to cool, then drizzle over salad.