Homemade Minestrone Soup

Name: Homemade Minestrone Soup
Ingredients: 3 tablespoons olive oil; 1 medium onion, chopped; 2 carrots, peeled and chopped; 1 large celery rib, chopped; 1 teaspoon minced garlic; 2 cups cubed white, red, our Yukon gold potatoes; Salt and pepper; 1 14.5 can diced tomatoes; 5 cups vegetable broth or water (you can also use chicken broth for a non-vegetarian option); 1 1/2 cups chopped green beans; 1 14 ounce can kidney beans, rinsed and drained; Handful of chopped fresh Italian parsley; Freshly grated Parmesan cheese