Place the pork in a large resealable plastic food storage bag and set aside.
In a bowl, combine the lime juice, orange juice, oregano, cumin, and 3 tablespoons of the minced garlic and whisk to combine thoroughly.
Pour the juice mixture over the pork and seal the storage bag. Place in the refrigerator to marinate overnight, turning occasionally.
The next morning, remove the pork from the refrigerator and allow it to return to room temperature while still in the bag before proceeding.
Position rack in center of oven and preheat the oven to 350?F. Line a roasting pan with aluminum foil and place a roasting rack inside the roasting pan.
Remove the pork from the marinade and discard the marinade. Season the pork with 1 tablespoon of the salt and the pepper.
Place the pork on the rack, fat side up. Cover with aluminum foil and bake for 4 hours. Start preparing the rice and beans and plantains.
Using oven mitts or pot holders, remove the foil from the roast and continue to bake until roast is very tender and pulls apart easily with a fork, about 2 hours longer.
Using oven mitts or pot holders, remove the pork from the oven and set aside to cool.
When the pork is cool enough to handle, remove any excess fat from the meat with a fork and discard. Using two forks or your clean hands, shred the pork into bite-size pieces. Set aside in a medium clean bowl.
PREPARING THE RICE AND BEANS AND PLANTAINS:
While the pork is roasting, in a medium saucepan combine the canned, undrained black beans, 2 tablespoons of the vegetable oil, 2 teaspoons of the salt, and the water and bring to a boil over high heat.
Using a wooden spoon, stir in the rice and return to a boil. Cover the pan with a tight-fitting lid and reduce the heat to medium-low so that the rice just simmers. Cook until the rice is tender and has absorbed the cooking liquid, about 20 to 25 minutes.
Meanwhile, to peel the plantainsówhich do not peel like regular bananas, top to bottomócarefully run a sharp knife down the length of the plantain in several spots. Then you can simply peel away the skin by opening it side to side.
Slice the peeled plantains crosswise on a diagonal into 1/2-inch-thick slices.
In a large skillet, heat the remaining 1/4 cup of vegetable oil over medium-high heat and sautÈ the plantain slices, in batches if necessary, until golden brown on both sides, turning with tongs to ensure even browning, about 1 1/2 to 2 minutes on each side. Transfer to plates lined with paper towels to drain briefly, then set plantains aside until ready to assemble the casserole.
In a small saucepan or skillet, heat the 1/2 cup olive oil over low heat and add the remaining 3 tablespoons of minced garlic. Cook slowly until the garlic is softened and very aromatic but not browned, about 4 to 5 minutes. Set aside to cool.
ASSEMBLING THE LASAGNA:
Position rack in center of oven and preheat the oven to 350?F.
When all of the elements are ready, spread half of the rice and bean mixture evenly along the bottom of a lasagna pan.
Top with the shredded pork, and season with 1/2 teaspoon salt. Top this with the fried plantains and season with the remaining 1/2 teaspoon of salt.
Place the remaining rice and bean mixture over the plantains and drizzle the reserved garlic oil mixture over the top. Cover with aluminum foil.
Using oven mitts or pot holders, place the lasagna in the oven until heated through, about 30 minutes.
Using oven mitts or pot holders, remove the lasagna from the oven and serve garnished with the cherry tomatoes and parsley.
YIELD: 12 to 16 servings