Gnocchi with Sage and Burnt Butter

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1. 1Step 1: Preheat the oven to 400°F.
2. 2Step 2: Pierce the skins of the potatoes all over, spread them over a baking tray, then bake in the oven for 1 hour, or until soft.
3. 3Step 3: Cut the potatoes in half while still piping hot, then scoop out the flesh and pass through a strainer. Do not overwork them or they will turn gloopy. Let the potatoes cool slightly, then sprinkle over the flour and cornstarch, chopping together with a dough scraper to incorporate. Add the egg yolks and chop again. Once well combined, bring the dough together with your hands and knead gently for a couple of minutes until smooth. Cover with cheesecloth and leave to rest for 5 minutes.
4. 4Step 4: Lightly flour a work surface and cut the dough into 4 equal-sized pieces. Roll each of these into a ¾-inch-thick log, then cut into even ¾-inch-long pieces.
5. 5Step 5: Bring a large saucepan of salted water to a boil. Add the gnocchi and cook until they float to the surface of the water.
6. 6Step 6: Drain the gnocchi, then chill in a large bowl of iced water to cool. Drain again, cover and store in the fridge until needed. They will keep for up to 2 days.
7. 7Step 7: Put the olive oil in a large frying pan and set over a medium heat. Once hot, gently add some of the gnocchi, being careful not to overcrowd the pan. Cook undisturbed for a couple of minutes until golden, then use a spoon to flip each individual gnocchi and cook them on the other sides too. Remove from the pan and cook the next batch of gnocchi in the same way. When they are all golden, return them all to the pan.
8. 8Step 8: Add the butter and cook until browned: it will be foaming and smell nutty. Add the zest of the lemon. Use a slotted spoon to remove the gnocchi from the pan while you cook the sage.
9. 9Step 9: Working quickly, add the sage leaves to the butter and cook for about 30 seconds until they crisp up. Use the slotted spoon to remove the leaves to a plate.
10. 10Step 10: Return the gnocchi to the butter in the pan and add the hazelnuts. Heat gently until all is heated through, spooning the butter over the gnocchi, then squeeze over the lemon juice. Top with the crispy sage, Parmesan and black pepper and serve immediately.