Country Ham with Stone-Ground Grits and Redeye Gravy

["In a large heavy-bottomed saucepan, bring 4 cups of water to a boil over medium-high heat.", "Stir in the grits and return to a boil.", "Season with 1 teaspoon kosher salt.", "Decrease the heat to low and simmer until creamy and thick, stirring often, 45 to 60 minutes.", "Heat a large cast-iron skillet over medium-high heat.", "Add the country ham and cook until crisped and golden brown on each side, about 5 minutes.", "Remove the ham and keep warm.", "Add the coffee and 1 cup water to the skillet, scraping up any brown bits with a wooden spoon.", "Simmer until the ""gravy"" has reduced to about 1/2 cup, 3 to 5 minutes.", "Spoon the hot grits into warmed bowls.", "Top each with a pat of butter and black pepper to taste.", "Top with the ham and ladle over the gravy.", "Serve immediately."]