Position a rack in the center of the oven and preheat to 400 degrees F.
For the sauce: Heat the oil in a heavy medium saucepan over medium heat. Add the garlic and onions. Add 1 teaspoon salt and 1/2 teaspoon pepper. Cook until the onion is tender, about 4 minutes. Stir in the cocoa powder. Add the broth, rosemary, vinegar and tomatoes. Bring the sauce to a simmer. Cover the pan. Reduce the heat to low and simmer for 10 minutes, stirring occasionally. Season with salt and pepper. Remove the pan from the heat.
For the pork: Whisk the cocoa powder, allspice, dark brown sugar, salt and pepper in a small bowl to blend.
Place the pork on a heavy nonstick baking sheet. Rub the allspice mixture over the pork. Drizzle with olive oil and roast until a thermometer inserted into the center of the pork registers 145 degrees F, 25 to 30 minutes. Tent loosely with foil and let rest 10 minutes.
Cut the pork crosswise into 1/2-inch-thick slices. Arrange the slices on a platter. Spoon the sauce over the pork and serve.