In a medium saucepan cover potatoes with water and add 2 tsp. salt. Bring to a boil and simmer on high for 5 minutes to parboil. Drain and set aside.
In a large nonstick skillet heat 1 tbsp. butter over medium heat. Fry sausages about 4 minutes per side until golden brown. Depending on the size of your skillet, you may have to do this in two batches. Remove sausages to plate and cover with foil to keep warm.
Add additional tablespoon of butter and tablespoon of olive oil to the skillet. Add drained potatoes and cook for 5 minutes, stirring occasionally. Add onion, apples, 3/4 tsp. salt, 1/4 tsp. pepper to skillet. Cook 12-15 minutes, using a silicon spoon to stir, flip occasionally, and scrape up pieces on bottom of skillet until apples are crisp tender and potatoes are cooked through.
Sprinkle cheese on top of hash, place sausages on top, and cover with lid to warm briefly and melt cheese. Combine honey and mustard to serve with sausages and hash.
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