In a small mixing bowl, combine the lemon zest, fresh lemon juice, grated garlic, kosher salt, and black pepper. Whisk together until well mixed, then slowly drizzle in the olive oil while whisking until smooth.

Using a vegetable peeler or mandoline, shave the zucchini into thin ribbons and transfer to a large mixing bowl, gently separating them.

Pour the lemon vinaigrette over the zucchini ribbons and toss gently to coat. Let sit for 15-20 minutes at room temperature.

Fold in half of the basil and hazelnuts. Transfer salad to a platter, topping with remaining basil and hazelnuts, and shave Parmigiano Reggiano over the top.