In a large pot, heat oil and butter over medium heat and saute onions until translucent (about 4-5 minutes). Add garlic and cook another 30 seconds.
Stir in the whole tomatoes (break apart tomatoes with hands or the back of wooden spoon), chicken broth, tomato paste, brown sugar, baking soda, salt, pepper, oregano, and bay leaf. Bring to a simmer over medium to medium-low heat for 10-15 minutes until thickened and then remove from the heat.
Add the cream and basil leaves and puree in batches in a blender or with a hand blender until smooth. Serve garnished with fresh basil and grated Parmesan or Asiago cheese and a side grilled cheese sandwich.
Recipe makes about 4 large bowls of soup or 6 cup size servings. Keep leftovers for up to 4 days in fridge or 3 months in the freezer.