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1
In a large, heavy-bottomed saucepan, heat the oil over high heat until smoking.
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2
Add all the chicken parts and brown all over, stirring to avoid burning.
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3
Remove the chicken and reserve.
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4
Add the carrots, onions, and celery to the pot and cook until soft and browned.
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5
Return the chicken to the pot and add 3 quarts of water, the tomato paste, peppercorns, and parsley.
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6
Stir with a wooden spoon to dislodge the browned chicken and vegetables bits from the bottom of the pan.
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7
Bring almost to a boil, then reduce heat and cook at a low simmer until reduced by half, about 2 hours, occasionally skimming excess fat.
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8
Remove from heat, strain, and press on the solids with the bottom of a ladle to extract out all liquids.
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9
Stir the stock to facilitate cooling and set aside.
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10
(Refrigerate stock in small containers for up to a week or freeze for up to a month.)
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11
In a large shallow bowl, cover the bread with the milk.
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12
Allow to sit for 10 minutes.
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13
Squeeze the milk from the bread by hand, cut the bread into a coarse dice and place in a medium bowl.
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14
Add the prosciutto and 1 cup Parmigiano-Reggiano, egg yolks, parsley, and salt and pepper and roll into balls the size of a quarter.
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15
Roll each ball in the egg whites, then the breadcrumbs.
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16
In a heavy-bottomed skillet, heat the oil until almost smoking.
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17
Cook the balls until golden and remove to a plate lined with paper towels.
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18
When they?ve drained, divide them evenly among six warmed soup bowls, pour the hot broth over them and serve with the remaining Parmigiano-Reggiano sprinkled over the top.