Place a large pot over medium-high heat with a little Olive Oil. Add the Onion and sauté until translucent. Next, add the Garlic and cook until fragrant; 1 to 2 minutes.
Add the Tomato Paste and stir to combine. Cook for an additional 1 to 2 minutes, stirring occasionally.
Then, add the Diced Tomatoes, Chicken or Vegetable Stock, Dried Oregano, Sugar, Salt, Pepper and Bay Leaf and stir to combine. Bring the mixture to a boil then reduce the heat to a simmer. Cook for 30 minutes to 1 hour.
Remove the pot from the heat and take out the Bay Leaf. Add the Half & Half and Fresh Basil. Purée until smooth with a stick blender or in batches in a conventional blender. If the soup is thicker than desired, you can thin it with a little Chicken or Vegetable Stock.
Adjust the seasoning, as desired, with Salt, Pepper and/or Sugar.
Keep warm until ready to use. Serve in a cup or bowl with a couple of sliced Fresh Basil Leaves.