To serve 4

Peel the plantains and cut each one lengthwise into a thick strip. In a heavy 10- to 12-inch skillet, melt the butter in 1 tablespoon of vegetable oil. When the foam begins to subside, add the plantain strips. Turning the strips with a slotted spatula, cook them for about 4 minutes on each side, or until they are lightly browned. As they brown, transfer the strips to paper towels to drain and cool.

In the same skillet, heat the annatto oil over medium heat. Add the ground beef and, mashing it constantly with the back of a spoon, cook until all traces of pink disappear. Add the onions, green pepper, chiles and garlic, and stir frequently, cook for 5 minutes until the vegetables are soft but not brown.

Stir in the ham, tomatoes, water, salt and a few grindlings of black pepper. Simmer, stirring occasionally, cook briskly until most of the liquid in the pan evaporates and the mixture thickens enough to hold its shape lightly in the spoon. Off the heat, stir in the olives, capers and vinegar, and taste for seasoning.

To make the pionono, shape each strip of plantain into ring about 3 inches in diameter, overlapping the ends by about ½ inch and securing them with a wooden toothpick inserted lengthwise. Lay the rings side by side in a shallow baking dish. Pour about ½ cup of the beef mixture into the center of each one. Pat the meat firmly into place and gently press the top as flat as possible.

In a small, shallow bowl, beat the eggs with a fork or whisk until they are thoroughly combined. One at a time, place the filled plantain rings on a slotted spatula and dip them into the eggs, coating them completely. Immediately slide each ring into the hot oil and deep-fry it for about 3 minutes, gently turning it about with a spoon until golden brown on both sides. As they brown, transfer the rings to paper towels to drain. Serve at once with rice and beans.