In a Dutch oven or heavy pot melt the butter and oil together over a medium heat. Add the onions and cook until softened
Add the tomatoes and chopped basil and season to taste with salt and pepper.
Add the chicken broth and reduce the heat to a simmer and cook for 15 minutes.
Allow soup to cool for approximately 45 minutes, then with an immersion blender, blend the soup until smooth.
If you plan on freezing the soup omit the next step and cool until it is ready to bag for the freezer. To freeze I put about 3 cups into a quart freezer bag, remove as much air as you can, seal and lay flat on a sheet pan. You will have 4 bags of soup with 2 servings in each. Freeze the bags on the sheet pan then transfer to freezer for storage.
Bring the soup back up to a boil, reduce the heat to low and slowly stir in the heavy cream. Serve immediately garnished with a sprig of basil.
If reheating from frozen, bring to a boil, reduce the heat to low and stir in 1/4 cup of heavy cream. Serve and garnish.