Heat the olive oil in a large pot over medium heat. Add the onion and garlic, and cook until softened, about 5 minutes.
Add the chicken or vegetable broth, diced tomatoes, tomato sauce, sugar, basil leaves, salt, and black pepper to the pot. Stir well and bring to a boil.
Reduce the heat to low and simmer for 10 minutes.
Stir in the milk and continue cooking until heated through.
Serve hot with some crusty bread on the side. Enjoy!