Heat a large saucepan to medium-low heat; add the oil. When the oil is heated, add the garlic and saute until lightly golden. Add the vinegar and saute an additional 2 minutes. Stir in the tomatoes, tomato paste, basil, sugar, salt and pepper. Bring the mixture to a simmer and stir occasionally until the tomatoes break down, about 8 to 10 minutes. Remove the pan from the heat and let it cool slightly. Place the sauce and cheese in a food processor and process until smooth. Taste the sauce and adjust seasoning as needed.