In a bowl combine the mozzarella, Parmesan and flour. Mix well to coat the cheese with flour. Set aside.
In a large saucepan, combine the garlic and wine (or broth), bring to a simmer over medium heat. Then reduce the heat to medium-low.
Add the cheese mixture by the handful to the saucepan, stirring constantly after each addition. Use a spoon and stir in a figure eight motion until the cheese is melted.
Stir in the tomatoes, balsamic vinegar, basil and oregano. Cook, stirring, until the tomatoes are heated through, about 2 minutes.