Heat olive oil in a 12-inch skillet over moderately low heat. Add garlic and sauté 1 minute to release its fragrance.
Add tomatoes and salt and pepper to taste. Cover and adjust heat to maintain a simmer. Cook until tomatoes are quite soft and have collapsed into a near-purée, about 10 minutes. Uncover and cook, stirring often, until mixture is very smooth, about 10 minutes. Add water as necessary to keep sauce from sticking.
Stir in cream. Taste and add sugar if sauce seems a bit tart. Simmer briefly to incorporate the cream, adding enough water to bring sauce to desired consistency. Taste and adjust seasoning.
Cook pasta in a large pot of boiling salted water until al dente. Drain, reserving about 1/2 cup of the cooking water. Transfer pasta to a large warm bowl. Add sauce, 2/3 cup Parmesan cheese and 1 tbsp of the parsley. Toss, adding a little of the reserved cooking water if necessary to thin the sauce.
Serve immediately on warm dishes, topping each serving with some of the remaining 1 tbsp parsley. Pass additional cheese at the table, if desired.