Cut the mozzarella into strips and set aside.
Wash and peel the eggplant, cut it into sticks, sprinkle a pinch of salt, toss and set aside for 20 minutes.
Roll 8 basil leaves into a cigar and slice about 1/8" thick. Set aside.
Meanwhile, peel the red onion, cut it into wedges and separate the layers.
Heat a tablespoon of oil in a large skillet. Add the eggplant sticks with the garlic and fry over medium to medium-high heat for 8-10 minutes, until lightly browned. Remove the eggplant and set them aside.
In the same skillet, fry the onion wedges with a drizzle of oil for about 5 minutes or until lightly browned.
Cut the tomatoes. Slice large tomatoes half-inch thick then quarter them. Cut medium tomatoes into wedges. Cut smaller tomatoes in halves. Leave small cherry tomatoes whole. Set aside.
Cook the fusilli pasta al dente in boiling water with a pinch of salt, drain, transfer to a large platter, spread around and let cool to room temperature.
In a large bowl, combine the pasta, tomatoes, eggplant, red onion, mozzarella, sliced basil and about 3/4 of the dressing.
Transfer to individual serving bowls, garnish with 1-2 whole basil leaves and drizzle with the remaining white balsamic vinaigrette. Serve right away.