Step 1 Heat oil in a medium skillet over medium heat. Cook and stir ham scraps until browned, about 5 minutes. Remove to a plate, reserving the grease in the pan.
Step 2 Place ham slices in the pan and cook over medium heat until browned, about 5 minutes on each side. Season both sides with salt, black pepper, and cayenne pepper. Remove ham and reserve on a plate.
Step 3 Reduce heat to medium-low and sprinkle flour over the pan drippings. Cook and stir for 2 minutes. Increase heat to medium-high and pour in coffee into the pan. Cook and stir until combined and thickened. Season to taste. Return ham to the pan to warm through.