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1
In a food processor, pulse the flour with a pinch of salt.
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2
With the machine on, add the eggs, egg yolks and olive oil and process until the dough resembles coarse sand.
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3
Transfer the dough to a work surface and knead until smooth.
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4
Flatten the dough into a disk, wrap it in plastic and refrigerate for at least 30 minutes or up to 6 hours.
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5
In a medium saucepan, melt 2 tablespoons of the butter.
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6
Stir in the flour.
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7
Gradually whisk in the milk until the sauce is smooth, then bring to a boil over moderately high heat, whisking constantly.
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8
Reduce the heat to low and cook the sauce, whisking often, until no floury taste remains, about 10 minutes.
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9
Whisk in the cream and simmer for 3 minutes.
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10
Remove from the heat and stir in the proscuitto.
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11
Season the sauce with salt and pepper.
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12
In a large skillet, heat the olive oil.
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13
Add the porcini, season with salt and pepper and cook undisturbed over moderately high heat for 1 minute.
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14
Stir well.
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15
Reduce the heat to moderate and cook until the mushrooms release their juices, about 5 minutes.
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16
Continue cooking until all the juices have evaporated and the mushrooms begin to brown, about 5 minutes longer.
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17
Add the garlic and cook over moderately high heat until fragrant, about 2 minutes.
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18
Add the rosemary and season with salt and pepper.
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19
Preheat the oven to 425.
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20
Bring a large pot of salted water to a boil.
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21
Set a very large bowl of cold water nearby.
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22
Cut the pasta dough into 4 pieces and keep 3 of them wrapped.
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23
Run 1 piece of the pasta dough through a pasta machine, beginning at the thickest setting and working your way through successively narrower settings until you reach the thinnest.
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24
Cut the pasta sheet in half and drape it over a drying rack or the back of a chair.
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25
Repeat with the remaining 3 pieces of pasta dough.
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26
Cut the pasta sheets into 4-inch lengths.
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27
Cook half of the pasta in the boiling water for 1 minute.
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28
With 2 slotted spoons, transfer the cooked pasta to the bowl of water to cool for 2 minutes.
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29
Drain the pasta on paper towels.
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30
Repeat with the remaining pasta.
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31
Butter a 10-by-14-by-1 1/2-inch glass or ceramic baking dish.
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32
Cover the bottom of the dish with a double layer of pasta.
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33
Spread 1 cup of the proscuitto sauce over the pasta and scatter one third of the mushrooms and 1/4 cup of the Parmesan on top.
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34
Cover with a layer of pasta.
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35
Repeat the layering 2 more times, ending with a layer of pasta.
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36
Spread the remaining 1/2 cup of prosciutto sauce over the top and sprinkle with the remaining 1/4 cup of Parmesan.
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37
Drizzle with the melted butter.
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38
Bake the lasagne until bubbling and golden brown on top, about 25 minutes.
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39
Let the lasagna rest for 10 to 20 minutes before serving.
