Preheat the oven to 475?F.
Season the chicken with 1/2 teaspoon and 1/8 teaspoon of the cayenne. Season the onions and bell peppers with the remaining 1/2 teaspoon salt and the remaining 1/8 teaspoon cayenne.
Heat the oil in large skillet with an ovenproof handle, over medium-high heat. Brown the chicken, stirring constantly, 3 to 4 minutes. Add the andouille and cook, stirring constantly, for about 3 minutes. Add the onions and bell peppers. Cook for about 6† minutes, stirring constantly, or until the vegetables are soft and golden. Add the mustard and mix well. Add the potatoes. Brown and fold. With the back of a spoon, pat down the mixture into the bottom of the skillet. Cook for about 1 minute. Brown and fold and pat down the mixture again. Cook for 2 to 3 minutes, or until the potatoes are tender. Crack the eggs on top of the hash and bake, in the skillet, for 2 to 3 minutes, or until the eggs set.
Yield: 4 servings