Add tomatoes, celery, carrots, chicken broth, onions, oregano, basil and bay leaf to a large slow cooker (or heavy soup pot).
Cover and cook on low for 5-7 hours, until flavors are blended and vegetables are soft. (In my Le Cruset I cooked about 5 hours on the lowest setting.
About 30 minutes before serving prepare a roux. Melt butter over low heat in a skillet and add flour. Stir constantly with a whisk for 5-7 minutes. Slowly stir in 1 cup hot soup. Add another 3 cups and stir until smooth. Add all back into the slow cooker (or pot). Stir and add the Parmesan cheese, warmed Half & Half, salt and pepper. Add additional basil and oregano if needed (the slow cooker does a number on spices and they get bland over time, so don't be afraid to always season to taste at the end).
*Note: If you want to cut the butter and flour in half it still turns out delicious. I really think you could omit this step.