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1
Heat oil in heavy large pot over medium-high heat.
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2
Add veal bones and saute until deep brown on all sides, about 12 minutes.
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3
Transfer bones to bowl.
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4
Add onion, carrot, and celery to pot.
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5
Saute until browned, about 6 minutes.
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6
Add 2 cups cold water, tomato paste, herbs, and peppercorns; bring to boil, scraping up browned bits.
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7
Add bones with any accumulated juices, then remaining 10 cups water to pot.
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8
Bring to boil.
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9
Reduce heat to medium-low and simmer uncovered until stock is reduced to 2 1/2 cups, about 4 hours.
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10
Strain into 4-cup glass measuring cup, pressing on solids to extract as much liquid as possible.
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11
Refrigerate stock uncovered 1 hour.
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12
Spoon off fat from surface of stock.
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13
Place stock in heavy medium saucepan; add wine and simmer until reduced to 1 cup demi-glace, about 25 minutes.
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14
(Can be made 3 days ahead.
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15
Cover and chill.)
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16
Bring 2 cups water and mushrooms to boil in small saucepan.
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17
Remove from heat, cover, and let stand until mushrooms soften, about 20 minutes.
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18
Using slotted spoon, transfer mushrooms to medium skillet.
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19
Slowly pour soaking liquid into skillet, leaving any sediment behind.
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20
Boil over medium-high heat until liquid is reduced to glaze, stirring occasionally, about 6 minutes.
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21
Cool mushrooms.
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22
Transfer to work surface; chop mushrooms coarsely.
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23
Transfer mushrooms and any juices to large bowl.
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24
Add meat, salt, and pepper; mix gently.
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25
Shape mixture into six 1-inch-thick patties.
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26
Place on foil-lined baking sheet.
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27
(Can be made 1 day ahead.
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28
Cover and chill.)
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29
Preheat broiler.
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30
Rewarm demi-glace over medium-low heat; add butter and whisk until melted.
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31
Remove from heat.
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32
Place rolls, cut side up, on baking sheet.
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33
Broil until lightly toasted, about 2 minutes.
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34
Remove rolls; maintain broiler setting.
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35
Arrange roll bottoms on plates.
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36
Top with arugula.
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37
Heat 2 large broilerproof skillets over medium-high heat; brush with oil.
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38
Add 3 burgers to each skillet.
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39
Cook to desired doneness, about 5 minutes per side for medium-rare.
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40
Top each burger with slice of cheese.
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41
Broil burgers until cheese begins to melt, about 1 minute.
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42
Place burgers on roll bottoms; spoon some demi-glace over.
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43
Cover with roll tops.
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44
Serve, passing remaining demi-glace separately.
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45
*Dried porcini mushrooms are available at Italian markets, specialty foods stores, and many supermarkets