Cook onion, carrot, celery and garlic in a large pot with olive oil over medium heat until the vegetables have softened (about 5 minutes). Stir in the basil and oregano and cook for one more minute.
Pour in the cans of diced tomatoes and tomato sauce. Add chicken broth or 1 1/2 cups water plus 1 1/2 teaspoons chicken bouillon. Add the brick of frozen spinach. Allow the mixture to heat through, stirring occasionally to break up the spinach as it melts (about 10 minutes).
Once the soup is completely heated through, dice the Swiss cheese. Reduce the heat to low or turn the heat off completely. Drop in the Swiss cheese and stir it in. The cheese will melt and become gooey but remain in clumps. If the heat is left on high, the cheese will melt too much and dissolve in.