Heat oil in a large pot over medium-low heat. Add garlic; cook and stir until fragrant, 2 to 3 minutes. Add onion; cook and stir until slightly softened, 4 to 5 minutes. Add carrots and stir until heated through, 1 to 2 minutes.

Pour in chicken broth and diced tomatoes; bring to a boil, stirring frequently. Add red wine, reduce the heat to low, and stir in green beans, pinto beans, spinach, basil, oregano, salt, and pepper. Bring to a simmer, then reduce the heat to medium-low and continue to simmer until vegetables are tender, about 40 minutes.

Meanwhile, bring a large pot of lightly salted water to a boil. Cook seashell pasta in the boiling water, stirring occasionally, until cooked through but firm to the bite, about 8 minutes. Drain pasta, then stir into soup. Ladle soup into bowls and top with Parmesan cheese.