Wash the meat and add to a 5-qt. pot. Add 4 cups of water and boil, covered, until foam comes to the surface. Pour water out and rinse the meat and the pot. Return the meat to the pot, and add 4 cups of fresh water. Cover, and cook for 30 additional minutes. Soak rice in cold water while the meat cooks for the last 30 minutes.
After slicing the onion, peppers, and eggplant sprinkle with 1 teaspoon allspice, and 1 teaspoon salt.
Heat 1/4 cup oil in a medium-sized pan. Fry the onion and peppers until soft, set aside.
Next, fry the eggplant, adding more oil if necessary. If you prefer, you can spray the eggplant with cooking spray and bake in the oven instead.
Sprinkle potatoes with 1/4 teaspoon allspice and 1/4 teaspoon salt. Fry the potatoes, and drain on paper towels. Use more oil, as needed.
When the meat is tender, remove from the pot and add to the fried vegetables. Reserve the remaining broth.
Melt butter in the same pot. Add 2 tablespoons oil, 2 teaspoons salt, and 3 cups of reserved broth. If you don't have enough broth, add enough liquid to equal 3 cups. Add tomato paste and stir, over medium flame, until the tomato paste is dissolved.
Strain the rice and add to the pot with the tomato sauce. Stir to combine, then cover and cook on low, for 25 minutes, or until tender. Stir a few times during the cooking process.
Spray the bottom and sides of a 6-qt. Dutch oven with nonstick cooking spray. Place the tortilla on the bottom. The tortilla helps to keep the ingredients in place. Layer the meat, and vegetables over the tortilla. Add cooked rice and press down to compress it as tightly as possible. Reheat over low heat for an additional 10 to 15 minutes.
Cover the pot with a large platter. Quickly flip the pot over onto the platter to un-mold the rice. Remove the tortilla, and serve.