How to Make It
In a medium saucepan, heat 2 tablespoons of the oil. Add the onion and cook over moderate heat, stirring occasionally, until translucent, 5 minutes. Stir in the tomato paste and cook, stirring, until lightly caramelized, about 3 minutes. Add the rice and 1 cup of water; bring to a simmer. Cover and cook over low heat until the water is absorbed, about 5 minutes. Remove the saucepan from the heat. Stir in the chopped parsley, mint and sugar and season with salt and pepper. (The rice will not be fully cooked yet.)
Spread the grape leaves on a work surface. Spoon 2 tablespoons of the filling down the center of each leaf, leaving a 1-inch border on each side. For each stuffed grape leaf, fold the sides over the rice, then roll up the leaf into a log.
Scatter the parsley stems in a large skillet. Set the stuffed grape leaves on top in a single layer. Season with salt and add enough water to just cover the rolls. Bring to a simmer and cook over moderately low heat, uncovered, until the rice is tender, about 25 minutes. Drizzle the remaining oil over the grape leaves and let stand until cooled to room temperature. Serve.