To make the filling: Heat a large skillet over medium-high heat, add the beef and cook, stirring and breaking up clumps, until no pink remains, about 5 minutes. Add the onion, bell peppers, salt, black pepper, bay leaves, and achiote and cook until the vegetables are softened and the meat is browned, 6 to 8 minutes. Add the tomatoes and reserved juice, olives, tomato sauce, raisins, and vinegar and simmer, stirring occasionally, until the sauce is flavorful and most of the liquid has evaporated, about 35 minutes. Transfer the filling to a bowl to cool and set aside.

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

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

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

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

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