Preheat broiler and preheat a medium skillet over medium-high heat with 1 tablespoon oil and 1 tablespoon butter. Mix chicken with apple, syrup, grill seasoning, poultry seasoning, cinnamon and nutmeg and score the meat into 4 sections. Form 4 large, thin patties and set into hot butter and oil. Cook 5 minutes on each side.
Place fork split muffins on broiler pan and toast. Butter toasted muffins and reserve.
Heat a second nonstick skillet over medium heat and melt a tablespoon of butter in the pan. Beat eggs with milk, salt and pepper and scramble to desired doneness.
Pile 1 sausage patty, 1/4 of the eggs and Cheddar cheese on each of 4 muffin halves. Return muffins to broiler to melt cheese, 1 to 2 minutes, then set tops into place and serve.