Add the canned tomatoes, celery, carrots, chicken broth, onions, oregano, and basil to the slow cooker.
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. In a medium-sized pot, melt the butter over medium-low heat. Add the flour and whisk together until a paste forms.
Slowly whisk in 3 cups of the soup. Once this mixture heats and starts to thicken then 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.