For the burgers: Mix together beef, onion, bell pepper, garlic, cilantro, oregano, soy sauce, Worcestershire sauce, a scant 1/2 teaspoon salt, and 1/2 teaspoon pepper. Form into 4 (4 1/2-inch-wide) patties. Heat a large griddle or 12-inch heavy skillet over medium heat until hot, then lightly toast buns. Oil griddle, then cook patties, turning once, about 8 minutes total for medium-rare. Transfer to buns. Mix together cabbage, carrot, and 1/4 teaspoon salt, then cook, turning occasionally, until slightly wilted, about 2 minutes. Divide among burgers.
Oil griddle again, then sear onion and tomato, turning once, until slightly charred, about 2 minutes total. Divide among burgers. Stir together ketchup, mayonnaise, and mustard, then top burgers with sauce.
For the plantains: While the hamburgers are cooking, peel plantains and wrap them in foil. Place wrapped plantains on grill and cook until tender but still firm, slightly caramelized. Once cooked, remove from grill, and slice into 1/2-inch rounds, on the diagonal. In a small bowl, mix together the yogurt, mayonnaise, and chipotle peppers until smooth. Return the sliced pieces of plantains to the grill, and brush chipotle sauce on 1 side. Flip after a couple of minutes and brush the sauce on the other side. Remove from grill and serve with the burgers.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.