Heat oil in a Dutch oven over medium-high heat. Add onion to pan; sauté 3 minutes or until softened. Add oregano and garlic; sauté 1 minute. Stir in squash, zucchini, carrot, and corn; sauté 5 minutes or until vegetables are tender. Remove from heat.
Place 3 cups tomato and 1 can broth in a blender; process until smooth. Add tomato mixture to pan; return pan to heat. Stir in remaining 1 cup tomato and remaining 2 cans broth; bring mixture to a boil. Reduce heat, and simmer 20 minutes.
Add pasta and beans to pan; cook 10 minutes or until pasta is tender, stirring occasionally. Remove from heat. Stir in spinach, salt, and 1/2 teaspoon pepper. Ladle soup into individual bowls; top with cheese. Garnish with coarsely ground black pepper, if desired.