Step 1Trim the ends from the zucchini and cut them crosswise into 3-inch pieces. Julienne the pieces down to the core (discard the seeded core); then place the julienned strips into a large bowl.
Step 2Gently stir in the tomatoes and garlic, then stir in the sherry vinegar, olive oil, salt and pepper, tossing to evenly coat. Taste the slaw and adjust the flavor and seasoning as desired, then stir in the basil. The slaw can be made up to this point up to 3 hours in advance and stored, covered, in the refrigerator. This makes about 7 cups slaw.
Step 3Just before serving, stir in the pine nuts. Serve the slaw with a few shavings of Parmigiano over each portion.