Trim the skin off the ham, leaving as much of the fat as possible.

Soak the ham in enough milk to cover for about 20 minutes.

Drain and pat dry with paper towels.

In a large heavy skillet over moderate heat, brown the ham on each side, using a bacon press to keep the ham from curling and to help it cook evenly.

Remove the ham to a warm plate.

To deglaze the skillet, add the black coffee and cook, scraping up the brown bits that cling to the bottom of the pan.

Reduce the mixture over high heat for about 1 minute.

Pour the redeye gravy over the ham and serve hot with fried eggs.