In a 12-inch cast-iron skillet, heat 1 tablespoon butter over medium-high heat. Add ham; cook, turning once, until browned, 2 to 3 minutes per side. Remove from skillet, and let drain on paper towels. Reserve drippings in pan.
Add coffee to pan, scraping browned bits from bottom of skillet with a wooden spoon. Stir in broth, paprika, and sugar; cook, stirring occasionally, until thickened, about 4 minutes. Add remaining 2 tablespoons butter, swirling until combined; cook for 1 minute. Remove from heat. Stir in thyme. Serve over ham slices and Coffee Biscuits.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/red-eye-gravy-coffee-biscuits/