In a small pot, bring water, milk, and grits to a simmer covered with a lid. Season with salt and pepper. Whisk occasionally to prevent any sticking. Cook according to the instructions on the package until they are creamy. (Grits are done when they have a smooth, creamy consistency.) Stir in the butter and season with salt and pepper to your desired taste. Spread half of the cheese over top. Remove the grits from the heat and set aside with a lid on to keep warm.
Heat oil in a non-stick pan over medium heat. Carefully crack eggs on a flat surface and into the pan being careful not to break the yolk. Cook until the egg whites start to firm up then gently flip them using a spatula spread the remaining cheese over top and cook for another 30 seconds.
In a non-stick pan over medium heat, brown both sides of the chicken sausage. Toast the bread.
Serve the eggs and chicken sausage over grits with bread and apples. Garnish with chives.