Mince the garlic, dice the onion, peel and slice the carrots, and slice the celery. Add the onion, garlic, carrots, and celery to a large soup pot with the olive oil and sauté over medium heat for about five minutes, or until the onions are soft.
Add the tomato sauce, diced tomatoes (with juices), vegetable broth, basil, and oregano to the pot. Stir to combine, then allow the soup to come to a simmer.
Once the soup is simmering, add the frozen spinach (no need to thaw). Stir the spinach into the hot soup until it has melted and heated through.
Once the spinach is thoroughly mixed into the soup, give the soup a taste and add salt if needed. I did not add any, but this will ultimately depend on the sodium content of your canned goods and vegetable broth.
Dice the swiss cheese into small cubes. Add a small handful of cubes to each bowl, then ladle the hot soup over top. Serve and enjoy!