Wash hands with soap and water.
Scrub the onion with a clean vegetable brush under running water. Chop the onion and place in a bowl.
Scrub the apple with a clean vegetable brush under running water. Core the apple and slice it.
Heat butter over medium heat in a large nonstick sauté pan. Add the chopped onions. Cook onions until they are soft, about 5 minutes. Stir in apple jelly and brown sugar.
Remove wrapper from the sausage and add to the sauté pan.
Wash hands with soap and water after handling uncooked sausage.
Cook, uncovered, over medium-low heat until sauce has thickened, stirring occasionally, about 15-20 minutes.
Add apple slices to the pan. Cover and cook over medium-low heat until apples are tender, about 8-10 minutes.
Mix cornstarch and water in a small bowl until smooth. Stir mixture into sauté pan and bring to a boil. Cook and stir until thickened, about 1 minute. Serve warm.