Add tomatoes, tomato sauce, and next 7 ingredients (through broth) to a slow cooker/crockpot. Cover and cook for 2 hours on high or 4-8 hours on low. (If you are home, give it a stir every now and then and scrape down the sides)
About 30-40 minutes before serving transfer soup to a blender or food processor and puree until smooth, then return to crock pot.
Prepare the roux. Begin by melting the butter in a medium sauce pan over medium heat.
Add flour to melted butter and stir until flour clumps up. Slowly whisk in the heavy cream (or half & half) until mixture is thickened and smooth. Add roux and parmesan cheese to crockpot and stir to combine.
Allow to cook another 20-30 minutes until cheese is completely melted. Give it a good stir before serving. Top with additional basil and parmesan cheese if desired.