Put the mirlitons in a saucepan and cover with water. Boil, uncovered, for 30 to 35 minutes, or until fork tender. Drain and cool under tap water. Set aside.
Season the onions with the salt, black pepper, and cayenne. Heat the oil in a large skillet over medium-high heat, add the onions, and sauté for about 5 minutes, or until caramelized and golden. Add the butter and mirlitons and cook, stirring constantly, for about 5 minutes. Remove from the heat.
Yield: 4 servings