In a 10-inch cast-iron skillet over medium heat, cook the sausage until browned and the fat is rendered, about 10 minutes, breaking up the chunks of sausage with the back of a wooden spoon. Remove the sausage to a bowl and set aside.
Add 2 cups of the milk and 2 cups water to the skillet and bring to a boil. Whisk in the grits slowly until smooth and no lumps remain. Reduce the heat and continue to cook, whisking, until very thick, about 5 minutes. Remove from the heat and stir in about half of the grated cheese.
In a medium bowl, whisk together the eggs with the hot sauce and remaining 1 cup milk. Slowly stream the egg mixture into the skillet with the grits while continuously whisking. Fold in the cooked sausage, scallions and jalapeno and season with salt and pepper. Top with the remaining cheese and bake until a knife inserted in the center comes out mostly clean, 50 minutes to 1 hour.
Slice the reserved scallion tops and sprinkle on top just before serving.