In a slow cooker, combine tomatoes, celery, onion, carrots and broth. Cover and cook on low for 5-7 hours.
Forty five minutes before the soup is done, melt to butter in a deep skillet or large pot. Then whisk in the flour. Whisk for 5 minutes.
Slowly whisk in the half and half, followed by 1 -2 cups of the soup mixture from the pot. Whisk until smooth and well blended.
Then pour the flour/half and half mixture into the slow cooker with the remaining soup mixture.
Add the Parmesan cheese to the crock pot and stir soup to combine until cheese is melted.
Mix in salt, pepper, oregano, and basil. Cover and cook on low for 30 more minutes. Serve as is or blend with an immersion blender until smooth and serve. Serves 6-8