cheesy end of season garden minestrone

Name: cheesy end-of-season garden minestrone
Ingredients: 2 tablespoons olive oil; 1 cup chopped onion (about 5 ounces); 2 teaspoons chopped fresh oregano; 4 garlic cloves, minced; 3 cups yellow squash, chopped (about 13 ounces); 3 cups zucchini, chopped (about 13 ounces); 1 cup carrot, thinly sliced (about 4.5 ounces); 1 cup green beans, trimmed & cut into bite-size pieces (about 4.5 ounces); 4 cups plum tomatoes, cored & chopped, divided (about 22 ounces); 1 (48-ounce) can chicken broth, divided (or vegetable broth); 1 teaspoon kosher salt; 1/2 teaspoon freshly ground black pepper; 1/2 cup uncooked regular or gluten-free ditalini (very short tube-shaped pasta); 1 (15.5-ounce) can Great Northern beans, rinsed & drained; 1 (5-ounce) package fresh baby spinach; 1 cup shredded Asiago cheese (4 ounces); coarsely ground black pepper, for garnish (optional)