Heat oil in a medium saucepan over medium heat. Add the onion, pepper, and garlic; cook and stir 4 to 5 minutes or until vegetables are soft.
Add the cheeses, cream, and milk; heat mixture until cheeses melt and the mixture is simmering.
Stir in the tomatoes (including their liquid), tomato juice, basil, sugar, and pepper. Continue to simmer mixture for 15 to 20 minutes while stirring constantly. Do not boil.
