Step 1

Cut the onion and bell pepper into small dice, placing them in a medium bowl. Season them with half of the salt and half of the cayenne, stirring to coat evenly.

Step 2

Preheat the oven to 475 degrees.

Step 3

Heat the oil in a large, ovenproof skillet (preferably cast-iron) over medium-high heat.

Step 4

Trim the visible tendons and excess fat from the chicken, then cut the meat into 1/2-inch pieces and place it in a mixing bowl. Season evenly with the remaining salt and cayenne pepper. Coarsely chop the andouille (keeping it separate from the chicken).

Step 5

Add the chicken to the skillet. Cook for 3 or 4 minutes, stirring, until it loses its raw look. Add the andouille and cook for 3 minutes, stirring constantly (it should start to become fragrant), then add the onion-pepper mixture and cook for about 6 minutes, until the onions are softened and lightly golden.

Step 6

Stir in the mustard, then stir in the potatoes until well incorporated. Use the back of a spoon or a spatula to press down the hash mixture. Cook for 1 minute, then scoop and fold the mixture and press down again. Cook for about 6 minutes, stirring and pressing down with a spatula to maintain an even surface. Taste, and adjust the seasoning as needed.

Step 7

Crack the eggs one at a time, letting them fall on top of the hash with a little space between them and making sure the yolks remain intact. Immediately transfer the skillet to the oven and cook for 3 or 4 minutes or until the egg whites are just opaque.

Step 8

Divide the hash and eggs among individual plates. Top with a dash of hot sauce, if desired, and/or sprinkle with cayenne pepper. Serve warm.