Preheat the oven to 350°F. Lightly oil the inside of an 8x8-inch (2-quart) baking dish and set aside.
Cut off the ends of the plantains. Use a small knife to cut along the ridges of the plantain and remove the peels. Slice each plantain lengthwise in half then the halves in half so you end up with strips roughly 1/4-inch thick. Heat the 1 cup of oil in a dutch oven over medium heat. When the oil is hot fry the plantain strips in batches, until lightly browned, 1 to 2 minutes per side. Set the fried plantains on a paper towel lined plate and set aside. When all plantains are fried discard the oil and clean the dutch oven.
Add the beef, onion, and bell pepper to the now clean and empty dutch oven over medium heat. Cook while breaking up the beef until beef is browned and onions are softened, about 7 minutes.
Add the tomatoes, garlic, capers, cumin, 1 tsp salt, and 1/2 tsp pepper to the beef and onion. Stir to combine and cook, stirring occasionally, until most of the liquid in the pan has evaporated, about 10 minutes.
Take the beef mixture off the heat and stir in the sliced olives. Season with salt and pepper to taste if necessary.
Lay one-third of the plantain slices in the bottom of the baking dish. Spread half the beef mixture evenly on top. Sprinkle half the cheddar cheese on the beef mixture. Lay half of the remaining plantains on top then spread on the remaining beef mixture and sprinkle on the remaining cheddar cheese. Lay the remaining plantains on top. Whisk the eggs in a small bowl and pour evenly over top of everything.
Bake in the preheated oven, uncovered, for 30 minutes.
Sprinkle the Monterey jack cheese on top and bake an additional 10 minutes or until cheese is melted.
Take out of the oven and let sit for 5 minutes before serving.
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