Boil the potatoes in their skins in salted water for about 20 minutes, or until they are completely tender.
Peel the potatoes while still warm, then mash them thoroughly using a potato ricer or a fork in a bowl.
Let the mashed potatoes cool slightly, then add the egg, salt, and flour. Knead until you have a soft, non-sticky dough.
Divide the dough into several portions and roll them into logs. Using a sharp knife, cut the logs into approximately 2 cm pieces.
Bring a large pot of salted water to a boil. Cook the gnocchi in small batches until they float to the surface (about 2 minutes), then drain them.
In a skillet, melt the butter, then sauté the diced green apple and brown sugar until the sugar caramelizes and the apple softens.
Pour in the heavy cream and honey, then stir in the cinnamon. Allow the sauce to thicken slightly.
In a separate skillet, dry-toast the roughly chopped walnuts until fragrant.
Pour the apple-caramel sauce over the cooked gnocchi, then gently toss to coat each piece.
Sprinkle with the toasted walnuts for extra crunch and rich flavor.
Serve immediately while warm, drizzled with a little extra caramel sauce and sprinkled with walnuts!
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