In a medium saucepan over moderate heat, melt the butter. Add chicken and brown skin side down. Turn over and add chopped onion. Cook until soft and starting to color about 6 to 8 minutes. Cover with chicken stock, and add the coffee and brown sugar, if using. Reduce heat to medium and cook the red eye gravy until thick enough to coat the back of the spoon, about 2 to 4 hours. Strain stock into a large bowl and reserve. The chicken can be used for another recipe or discarded.
Preheat a large heavy bottomed frying pan over medium-high heat. Season ham steaks with black pepper and add to the hot skillet. Cook until golden brown on each side, 6 to 8 minutes and transfer to serving plates.
In the same skillet, once steaks have been removed, reduce heat to medium and fry the eggs to desired doneness.
Cover the steaks with red-eye gravy and crown with a fried egg. This dish can be served with potatoes, hash browns or biscuits, if desired.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.