2 cups whole milk
1 cup stone-ground grits
Coarse salt and freshly ground black pepper
12 ounces mild pork or turkey sausage
1 cup grated sharp Cheddar (about 4 ounces)
1 tablespoon unsalted butter, plus more for the dish
1/4 teaspoon cayenne pepper
4 large eggs, lightly beaten
2 green onions, white and green parts, chopped
1 jalapeno chile, seeded and finely chopped