Sprinkle in the flour, and stir to cook the flour for 1 minute. Will look like a paste. Slowly stir in the chicken stock, whisking the whole time so the flour doesn't clump. Then add the canned tomatoes, basil and garlic. You can either transfer to a slow cooker and cook over low for 4 hours or high for 2 hours, or cook it on the stove top by bringing it to a boil, then cover and reduce heat to low and cook for 20 more minutes.
Remove the lid, and either use an immersion blender or stand blender (careful when blending hot liquids in a stand blender!). Blend until the soup is creamy. Then stir in the parmesan cheese and heavy cream. Heat soup for another 5-10 minutes, or until the cheese is melted and the soup is warm. Taste for salt and pepper.