In a large pot, heat the olive oil over medium-low. Stir in the onion, carrots and garlic and cook until vegetables are tender, about 7 minutes.
Stir in the tomato sauce, diced tomatoes, chicken broth, butter, oregano, basil, salt, pepper, red pepper flakes, thyme, and the baking soda. Increase the heat until the soup simmers, then reduce to low and simmer for 30 minutes.
Remove from heat, allow to cool slightly before stirring in the half and half.