Bring a medium pot of salted water to a boil. Add the rice and cook until partially tender, about 10 minutes. Drain well and set aside.
Heat a large skillet over medium heat. Add the pine nuts and toast, stirring frequently, until golden, 2 to 3 minutes. Transfer to a plate.
Add the olive oil and onions to the skillet and cook, stirring occasionally, until deeply golden and softened, 12 to 15 minutes. Stir in the date syrup, then add the ground beef and cook, breaking it up with a spoon, until browned and cooked through.
Stir in the prunes, apricots, toasted pine nuts, mint, pomegranate molasses, cooked rice, salt, baharat, cinnamon, and black pepper. Cook until the mixture is fragrant and evenly combined, about 2 minutes. Remove from the heat and let cool slightly.
Heat the oven to 350°F/180°C.
Arrange the chicken thighs smooth-side down on a work surface. Spoon about 2 tablespoons filling onto the lower edge of each thigh and roll tightly. Arrange seam-side down in a 9-by-13-inch baking dish.
In a medium bowl, whisk together the water, tomato paste, pomegranate molasses, date syrup, salt, baharat, and cinnamon. Pour the sauce evenly over the chicken. Cover tightly with parchment paper and aluminum foil.
Bake until the chicken is very tender and the rice filling is fully cooked, about 1½ hours. Remove the foil and parchment and continue baking until the tops are lightly caramelized and the sauce has reduced slightly, 20 to 25 minutes more. Serve hot with spoonfuls of the sauce.