Heat a large skillet over medium heat, then add the oil, celery, carrots and onions; cook 5 to 6 minutes, or until golden. Add to slow cooker.
Pour the juice of the tomatoes into the slow cooker, then roughly crush the tomatoes with your hands; add to slow cooker. Then add chicken (or vegetable broth), thyme, basil, and bay leaf.
Cover and cook on LOW for 6 hours, until the vegetables get soft and the flavors blend. Using an immersion blender, blend the soup until smooth (or you can carefully do this in small batches in the blender).
Melt the butter over low heat in a large skillet and add the flour. Stir constantly with a whisk for 4 to 5 minutes. Slowly whisk in about 1 cup of the hot soup, then add the 1 3/4 cups of warmed milk and stir until smooth. Pour back into the slow cooker and stir, add the grated Romano cheese and adjust salt and pepper, to taste.