With a sharp knife, trim the excess fat from the ham slices and cut the fat into small bits.
Place the fat in a heavy, ungreased 12-inch [30-cm.] skillet and, stirring frequently, fry over medium heat until the bits are crisp and have rendered all their fat.
Discard the bits of fat.
Fry the ham in the rendered fat, turning the slices so that they color evenly.
Transfer the fried ham to a warmed platter and pour the coffee into the skillet.
Bring to a boil over high heat, meanwhile scraping in the brown bits that cling to the bottom of the pan.
Boil briskly, uncovered, until the gravy turns red, then pour it over the ham and serve at once.
Ham with red-eye gravy is a favorite breakfast dish, traditionally served with boiled grits or hot biscuits—or both.