Pasta with Summer Squash and Chorizo

Name: Pasta with Summer Squash and Chorizo
Ingredients: 9 small Gold Bar or summer squash (about 2 3/4 pounds), divided; 1/4 cup plus 3 tablespoons extra-virgin olive oil , plus more for drizzling, divided; 1 large white onion, thinly sliced (about 2 cups); 2 large carrots , peeled and thinly sliced (about 1 1/2 cups); 6 garlic cloves , sliced (about 1/4 cup); 1 tablespoon water (optional); 4 cups vegetable broth; 1 (8-ounce) beefsteak tomato , chopped (about 1 1/2 cups); 1 teaspoon kosher salt , divided; 12 ounces lumache or other short pasta such as conchiglie, penne, or ziti; 12 ounces fresh Mexican chorizo; 1/4 cup torn fresh basil , plus more for garnish; Finely chopped fresh chives; Grated Grana Padano cheese; Aleppo pepper