Grilled Zucchini Pasta Salad with Burst Cherry Tomatoes

Name: Grilled Zucchini Pasta Salad with Burst Cherry Tomatoes
Ingredients: 1 pound dry, short pasta, such as orecchiette, fusilli, or farfalle; 2 tablespoons olive oil; 2 medium zucchini (about 12 ounces), trimmed and cut lengthwise into 1/4-inch thick slabs; 1 pint cherry or grape tomatoes (about 2 cups); 1/2 teaspoon kosher salt, plus more for the pasta water; 1/2 teaspoon freshly ground black pepper; 5 skewers, soaked in water at least 30 minutes if wooden; 6 tablespoons store-bought Parmesan and roasted garlic dressing, such as Newman’s Own, divided; 1/4 cup chopped fresh chives; 1/4 cup finely grated Parmesan cheese (optional)