Heat a large skillet over medium high heat, add beef and cook, stirring and breaking up clumps, until no pink remains, about 5 minutes.

Add onion, chopped red and green bell peppers, salt, pepper, bay leaves, and achiote, and cook until vegetables are softened and meat is browned, 6 to 8 minutes. Add tomatoes and reserved juice, olives, tomato sauce, raisins, and vinegar and simmer, stirring occasionally, until sauce is flavorful and most liquid has evaporated, about 35 minutes. Transfer filling to a bowl to cool and set aside while you prepare the plantains.

Peel plantains and cut diagonally into 1/3-inch slices. In a large skillet heat 1/4 cup of the oil over medium high heat and saute plantains in batches until golden brown, about 2 minutes on each side, adding remaining oil as needed. Transfer cooked plantains to paper towels to drain.

Preheat oven to 350 degrees F. Lightly oil a 3 quart baking dish or casserole.

In a small bowl, whisk eggs and water until blended.

Pour half of egg-water mixture into baking dish and layer bottom and sides of dish with 1/3 of the plantains. Spread half of the beef filling over the plantains and sprinkle with half of the Parmesan. Top with half of the remaining plantains and then spread remaining beef filling, topping with remaining Parmesan, and ending with remaining plantains. Pour remaining egg-water mixture over top of pie, tilting to distribute evenly.

Cover baking dish with aluminum foil and bake in middle of oven until hot throughout and bubbly around edges, about 1 hour. Cool for 10 minutes before serving pie. (Pie can be inverted onto a serving platter for a nice presentation.)