To make the grits, heat oven to 350°F.
In a saucepan, bring milk and butter to a boil over medium-low heat. Whisk in the stone-ground grits, salt and pepper. Cook and stir constantly for 8-10 minutes or until very thick.
Remove from heat and stir in 1 cup of Cheddar cheese and 1 egg. Allow to rest for 10 minutes while you heat the cast-iron skillet.
Grease a cast-iron skillet with vegetable shortening and place in the preheated oven for 10 minutes. Carefully remove the skillet and add the grits, spreading to cover the bottom. Return skillet to oven and bake for 25 minutes.
To make the quiche, while the grits bake, cook the sausage links on a griddle or skillet as directed on the package. Remove to drain on paper towels.
In a large bowl, whisk the eggs, heavy cream, milk, salt and pepper together. Stir in cheese.
Remove grits from oven and reduce the temperature to 325°F.
Arrange sausage links on top of grits in wagon wheel pattern. (If you prefer, you may chop the sausage links and sprinkle all over top instead.) Pour the egg mixture evenly over top and sprinkle with the green onions and a dash of red cayenne pepper.
Return to the oven and bake for 30 minutes, or until set. Allow to set for 10 minutes before serving.