In a saucepan, over medium heat, add the milk and butter. Season with salt and pepper. Bring the liquid to a boil. Whisk in the grits. Stir constantly for 6 minutes or until tender.
Set aside and keep warm. Heat a skillet over medium heat. When the pan is hot, add the ham and sear for 4 to 5 minutes on each side. Remove the ham from the pan and set aside. Stir in the coffee. Bring the liquid to a simmer and cook for 2 minutes. Remove from the heat. To serve, cut the ham into four portions. Spoon the grits in the center of each plate. Lay each piece of the ham next to the grits. Spoon the gravy over the ham. Serve with toast.