For the grits, bring the water and milk to a boil in a pan, whisk in the polenta, and then reduce the heat and cook for an hour. Season with salt and pepper and set aside.
For the poached eggs, bring a pan of water to a gentle simmer and add salt and vinegar. Using a spoon, swirl the water in a circle and crack the eggs into the center of the water. Simmer for about 2 minutes. Set aside.
For the gravy, to a pre-heated skillet, add a slice of ham and warm it through. Then remove the ham to a plate. Into the same skillet add the coffee and pork stock and reduce.
To a bowl or plate add a serving of grits, the ham, a poached egg and sprinkle with chives. Drizzle the red-eye gravy over the grits and serve.