Heat a large cast-iron skillet or heavy saucepan
over medium-high heat and melt
the butter. Add the country ham steaks and sprinkle half of the brown sugar over each steak. Cook for about 1 minute. Turn the steaks and cook until the brown sugar begins to caramelize
, about 1 minute more. Remove from the pan and keep warm.
Deglaze the pan with the coffee, making sure to scrape up any brown bits, and simmer until reduced by about half. Plate the steaks and top with the redeye gravy.