Add tomatoes, celery, carrots, chicken broth, onions, oregano, and basil to your slow cooker. {If you want your soup more smooth and less chunky, pulse celery, carrots, and onion in a food processor until very fine. I did this so my veggies were more hidden in the soup.}
Cover and cook on low for 5-6 hours until flavors are blended and vegetables are soft.
About 30 minutes before the soup is ready prepare a roux.
Melt the butter over medium low heat in a skillet and add the 1/2 cup of flour. Whisk together constantly for 5-7 minutes.
Slowly add 1 cup of soup. This will start to form a thick paste. Slowly add another 3 cups of warm soup. Add this back to the slow cooker.
Stir in the parmesan cheese, warmed half and half, and salt and pepper. Add additional oregano and basil if needed.
Cover and cook on low for another 30 minutes.
You can also blend the soup in a blender at the very end to smooth the soup out if you would like.