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1
Preheat the oven to 400.
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2
Prick the potatoes once or twice with a small knife and bake for about 45 minutes, or until tender in the center when pierced.
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3
Let cool slightly.
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4
Peel the potatoes and pass them through a potato ricer or food mil into a large bowl.
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5
Let cool completely.
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6
Stir in the salt.
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7
Gradually stir in about half of the flour until the mixture becomes stiff.
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8
Transfer the mixture to a lightly floured surface and knead in as much of the remaining flour as necessary until the dough is no longer sticky.
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9
Line 2 baking sheets with wax paper and dust with flour.
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10
Divide the dough into 8 equal pieces.
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11
Set one piece on a floured surface; keep the remaining dough covered with an inverted bowl.
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12
using your hands, roll out the dough to a 1/2-inch-thick rope and then cut the rope into 3/4-inch lengths.
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13
Dip a fork in flour.
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14
Roll each piece of dough down the back of the tines; press gently with your thumb so the tines leave ridges.
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15
Alternatively, flatten the gnocchi by pressing each one gently with a fork.
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16
Set the gnocchi on the prepared baking sheets in a single layer without touching.
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17
Repeat with the remaining pieces of dough.
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18
Heat the olive oil in a large nonreactive skillet.
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19
Add the onion and cook over moderately high heat, stirring, until tender, about 5 minutes.
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20
Add the tomatoes and season with salt and pepper.
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21
Bring to a simmer, then reduce the heat to low and cook for 20 minutes, stirring occasionally.
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22
Bring a large pot of water to a boil.
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23
Stir in 2 tablespoons of salt, then add half the gnochhi, a few at a time, and simmer until they float to the surface.
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24
Using a slotted spoon, transfer them to a rack to drain thoroughly; don't pile them or they'll stick together.
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25
Repeat with the remaining gnocchi.
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26
Stir the prosciutto and basil into the tomato sauce.
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27
Spoon the gnocchi onto 4 large plates, top with the tomato sauce and serve.