Puree basil, shallot, white balsamic, water, sugar and salt in a blender, stopping as needed to scrape down side with a rubber scraper. With motor running, slowly pour in olive oil and puree until smooth. Season with freshly ground black pepper to taste. Set aside.
Using a vegetable peeler, shave zucchini into thin ribbons and gently toss with olive oil, lemon zest, lemon juice and a pinch of salt. Set aside.
Preheat oven to 350. Slice baguette on the diagonal about 1/2 inch thick. Brush with olive oil and season lightly with salt and pepper. Bake until crispy, about 10 minutes.
Arrange crostini on a plater and curl zucchini ribbons on top. Tear mozzarella into pieces and divide among the crostini. Drizzle with vinaigrette and sprinkle with freshly cracked black pepper to serve.