In large skillet, warm ½ tablespoon butter over medium-high heat. Add country ham and cook until browned, approximately 3 minutes per side.
Transfer browned ham to plate and set aside. Pour coffee into skillet and use spatula to scrape up any browned bits on bottom of skillet.
Pour in chicken broth. Reduce heat and simmer, uncovered, for 4 to 5 minutes, or until gravy is thickened. Add in remaining ½ tablespoon butter and whisk until melted.
Serve gravy warm over or on the side of browned ham on biscuits, similar to an au jus. Enjoy!