Preheat oven to 350°F. Sprinkle roasts on each side with salt, pepper, and 1 teaspoon sugar. Heat 2 tablespoons oil in heavy wide ovenproof pot over medium-high heat. Add roasts. Cook until brown, about 8 minutes per side; transfer to plate. Add 1 tablespoon oil and onions to pot. Saute until dark brown, stirring often, about 10 minutes. Mix in vinegar and allspice; boil until reduced to glaze, scraping up browned bits. Add broth, orange juice, and tomato sauce; bring to boil. Return roasts and accumulated juices to pot. Scatter dates around roasts; sprinkle with parsley. Cover pot; place in oven. Braise roasts 1 hour. Turn roasts over, cover, and braise until tender, about 1 hour. Tilt pot; spoon off fat from top of sauce. Cool uncovered 1 hour. DO AHEAD Can be made 2 days ahead. Chill uncovered until cold; cover and keep chilled. Preheat oven to 350°F. Transfer roasts to board, scraping sauce into pot. Cut crosswise into 1/2-inch-thick slices; overlap slices in baking dish. Spoon sauce over. Cover; rewarm about 25 minutes.