In a medium saucepan cover potatoes with water and add 1 teaspoon salt. Bring to a boil, lower heat, and simmer for 3-4 minutes, or until just fork tender. Drain and set aside.
In a large skillet heat oil over medium heat saute sausages about 3-4 minutes, or until golden brown. Remove sausage to a plate, leaving oil and drippings in the pan.
Add onions and apples to the skillet, cooking and stirring for 4 minutes, or until onions are tender.
Add butter to melt, then potatoes, thyme, ½ teaspoon salt, and ¼ teaspoon pepper. Toss to coat in butter and seasonings.
Sprinkle cheddar over potatoes and lay sausages on top. Remove from heat and cover for 5 minutes for cheese to melt and rewarm sausages.
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Notes
Potatoes - Any type of potatoes may be substituted. Try red potatoes, gold, or sweet potatoes.
Smoked sausage - Use beef, kielbasa, or turkey sausage for a healthier meal.
Apples - Golden delicious work well for sauteing because they don't break down or turn mushy. Granny Smith, Honeycrisp, or Jonagold will also work.
Cheese - I prefer sharp cheddar because the taste is more pronounced. Any cheese will work, though! Alternatively, leave off for a dairy free recipe.