In a large bowl, combine the tomatoes, sugar, ¼ cup of the oil, 1 teaspoon salt and ½ teaspoon pepper. Toss, then, using a potato masher, gently crush the tomatoes until they release some juice. Let stand at room temperature for at least 15 minutes or up to 1 hour, stirring occasionally.
To the tomato mixture, add the herbs and fold until incorporated. Stir in 1 cup of the ricotta; set aside. In a small bowl, stir together the remaining ricotta, the remaining 2 tablespoons oil, ½ teaspoon salt and ¼ teaspoon pepper; set aside.
In a large pot, bring 7 cups water to a boil. Stir in the pasta and 1 teaspoon salt, then cook, stirring often, until the pasta is al dente. Drain the pasta in a colander set in a large heatproof bowl. Shake the colander to remove as much water as possible, then add the pasta to the tomato-ricotta mixture; reserve the cooking water. Using tongs, toss to combine, adding reserved pasta water 1 tablespoon at a time until the sauce clings to the noodles.
Divide the pasta among individual bowls, drizzle with additional oil and serve, offering the seasoned ricotta and Parmesan cheese on the side.
