Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion, garlic and bay leaves and cook, stirring occasionally, until the onion is soft, about 6 minutes. Add the tomato paste, 1 1/2 teaspoons salt and 1/2 teaspoon pepper and cook, stirring, until the tomato paste turns brick red, about 5 minutes.
Add the bell peppers and cook, stirring occasionally, until they begin to soften, about 10 minutes. Add the wine and 1 cup water, increase the heat to high and bring to a boil. Reduce the heat to medium low, cover and simmer until the peppers are very soft, about 30 more minutes.
Uncover, increase the heat to medium and continue cooking, stirring occasionally, until most of the liquid has evaporated, 20 to 25 more minutes. Remove the bay leaves. Stir in the basil and balsamic vinegar and season with salt and pepper.