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1
Pour boiling-hot water over porcini in a bowl and let stand until softened, about 20 minutes.
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2
Lift out porcini, squeezing excess liquid back into bowl, and rinse to remove any grit.
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3
Finely chop porcini.
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4
Pour soaking liquid through a sieve lined with a dampened paper towel into another bowl and reserve.
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5
Trim leek, reserving about 5 inches of green leaves, and rinse greens well.
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6
Halve rest of leek lengthwise, then rinse well under cold water and pat dry.
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7
Coarsely chop greens and finely chop white and pale green parts, reserving greens separately.
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8
Finely grate enough cheese to measure 1/4 cup, then cut off and reserve rind.
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9
Reserve remaining piece of cheese.
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10
Pulse cremini caps, shiitake caps, 1/3 cup chopped porcini, white and pale green parts of leek, garlic, and 1/2 teaspoon salt in a food processor until finely minced.
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11
Heat butter in a 12-inch nonstick skillet over moderate heat until foam subsides, then cook mushroom mixture, stirring constantly, until liquid mushrooms give off is evaporated and mushrooms are golden, about 10 minutes.
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12
Transfer to a bowl and cool completely.
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13
Stir in 1/4 cup grated cheese, 1 tablespoon parsley, and salt and pepper to taste.
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14
Tuck parsley and thyme sprigs into celery and tie together tightly with string to make a bouquet garni.
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15
Bring cold water, beef broth, bouquet garni, cracked peppercorns, cremini stems, shiitake stems, leek greens, remaining chopped porcini, porcini soaking liquid, cheese rind, and remaining 1/4 teaspoon salt to a simmer in a 3-quart heavy saucepan, stirring occasionally.
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16
Reduce heat and cook at a bare simmer, partially covered, 45 minutes.
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17
Pour broth through a large sieve lined with a double thickness of rinsed and squeezed cheesecloth (or dampened paper towels) into a large bowl, pressing on and discarding solids.
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18
Return broth to saucepan.
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19
Set smooth rollers of pasta maker at widest setting.
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20
Cut pasta dough into 4 pieces and keep 3 pieces covered.
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21
Flatten unwrapped piece of dough into a rectangle and feed through rollers.
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22
Fold rectangle in half and feed through rollers 8 more times, folding in half each time and dusting with flour as necessary to prevent sticking.
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23
Turn dial to next (narrower) setting and feed dough through without folding.
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24
Continue to feed dough through without folding, making space between rollers narrower each time, until narrowest setting is used.
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25
(Cut sheet of dough in half if it gets too long.)
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26
Cut out as many rounds as possible from sheet with cookie cutter (reserve trimmings for another use, such as chicken noodle soup).
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27
Transfer rounds in 1 layer to a lightly floured wax-paper-lined baking sheet and cover with plastic wrap.
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28
Working with 5 pasta rounds at a time, put 1/4 teaspoon filling in center of each round, keeping remaining rounds covered tightly with plastic wrap.
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29
Moisten edges of filling-topped rounds with a fingertip dipped in water and fold in half, letting bottom edge protrude slightly beyond top edge, then press top edge to bottom half to seal.
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30
Holding straight edge of half-moon against nail of your little finger, wrap half-moon around fingertip (which will cause curved edge to flip up), overlapping corners and pinching to seal.
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31
Transfer tortellini to a dry kitchen towel (not terry cloth).
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32
Roll out and cut remaining dough and make more tortellini in same manner, working with 1 piece at a time.
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33
Bring broth to a boil and season with salt and pepper.
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34
Add tortellini and cook at a strong simmer, stirring gently once or twice, until tender, 3 to 5 minutes.
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35
Ladle broth with 8 to 10 tortellini per person into bowls and serve remaining piece of Parmigiano-Reggiano on the side for grating.