In a heavy 4-quart stockpot, heat the oil over low heat. Add the onion and fry until soft and clear, about 5 minutes. Add the garlic and continue to fry for another 3 to 5 minutes. Add the rice and stir well. Fry slowly without moving it too much, about 10 minutes. Stir in the hot chicken stock and the hierbabuena or mint. Add salt and pepper to taste. Cover and let cook for 15 to 20 minutes, or until all the stock is absorbed. Do not peek at or stir the rice during the cooking process.
Cut the plantains in half. Cut each half lengthwise into 1/4-inch thick slices (about 4 to 5 slices). In an 8-inch cast-iron frying pan, heat the oil until smoking. Add the plantains and fry 3 to 5 minutes on each side or until brown. Remove them from the oil and drain on paper towels. Mound the rice on a plate or a platter and serve with the fried plantains on top.