Bring the rice and 4 cups of water to a boil in a saucepan over high heat. Reduce heat to medium-low, cover, and simmer until the rice is tender, and the liquid has been absorbed, 20 to 25 minutes.
Place the egg into a saucepan, and cover with water by 1 inch. Cover the saucepan and bring the water to a boil over high heat. Once the water is boiling, remove from the heat and let the egg stand in the hot water for 15 minutes.
Pour out the hot water, then cool the egg under cold running water in the sink. Peel once cold. Chop the egg and set aside in a small bowl.
Heat 1 cup of vegetable oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C). Deep fry the potato cubes until golden brown, about 5 minutes; drain on paper towels, and set aside.
Place tomatoes and 1/2 cup of water in a blender, and puree until tomatoes are liquefied (peel and seed first, if desired).
Heat 1 tablespoon of vegetable oil in a large skillet over medium heat, and cook and stir the onion, garlic, aji chile powder, cumin, black pepper, and oregano until the onion begins to brown, 8 to 10 minutes; pour in the pureed tomatoes, and simmer for 5 more minutes, stirring often.
Mix in the ground beef and carrots, and cook until the meat is no longer pink and the carrots are tender, about 10 minutes. Break the meat up into small chunks as it cooks.
Mix in the chopped hard-cooked egg, peas, and peanut butter until thoroughly combined. Finally, gently stir in the cubes of fried potato.
To assemble the dish, oil a flexible plastic bowl (at least 1 cup size) and press cooked rice into the bottom to fill 1/3 of the bowl.
Layer about 3/4 inch of meat mixture over the rice, and top with more cooked rice to fill the bowl. With an oiled hand, gently press on the rice to compact the mixture; place a serving plate on top of the bowl, flip, and turn out the rice and meat-filled form. Repeat with remaining ingredients.
Garnish with sprinkles of cilantro, chopped tomato, and dollops of ketchup on each serving.
