Heat a skillet over medium heat, and melt 2 tablespoons butter. Add onions and cook, stirring occasionally, until browned and just a bit crispy around the edges, 20 to 25 minutes.
Meanwhile, add potatoes and apples to a large saucepan filled with just enough generously salted water to cover them by about 1 inch. Bring to a low boil over medium heat. Cook until potatoes and apples are fork tender, 10 to 15 minutes. The apples will soften more quickly than the potatoes.
Drain potato-apple mixture and return to the saucepan. Stir in remaining butter, sugar, garlic powder, salt, pepper, and nutmeg, and mash to your preference, either chunky or smooth.
Cover the saucepan to keep warm. Spoon onions over potatoes to serve.
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