In a 10-inch cast-iron or nonstick skillet heat the oil and 1 tablespoon of the butter over medium heat. Add potatoes in an even layer. Cook 8 minutes, stirring occasionally, until lightly browned. Stir in half the thyme and 1/4 teaspoon ground black pepper. With a wide metal spatula press down firmly. Cook about 8 minutes more or until potatoes are tender.
Meanwhile, in a medium skillet melt remaining 1 tablespoon butter over medium heat. Add sausage and apple. Cook, stirring occasionally, for 10 minutes or until apple is tender. Stir in remaining thyme.
Unmold potatoes onto serving platter; top with apple mixture. Add salt to taste. Makes 4 servings.