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1
In a large saucepan, cover the chicken wings with 10 cups of water.
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2
Add the carrot and celery and bring to a boil.
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3
Skim, add a few pinches of salt and simmer over low heat for 1 1/2 hours.
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4
Strain the stock and skim off the fat.
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5
Measure out 1/2 cup of stock and set it aside.
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6
Heat the 3 tablespoons of olive oil in a large saucepan.
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7
Add the scallions and cook over moderate heat until softened, about 3 minutes.
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8
Add the onions and cook over low heat, stirring occasionally, until softened, about 8 minutes.
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9
Add 2 quarts of the chicken stock and a pinch of salt and simmer over low heat until the onions and scallions are very soft, about 15 minutes.
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10
Working in batches, puree the soup in a blender until very smooth.
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11
Pour the soup into a clean saucepan and season with salt.
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12
Heat the remaining 2 teaspoons of olive oil in a medium saucepan.
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13
Add the potato, garlic and a pinch of salt and cook over low heat, stirring, until the potato pieces are glazed, about 2 minutes.
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14
Add the reserved 1/2 cup of chicken stock and 1/2 cup of water and simmer over moderately low heat until most of the liquid has evaporated and the potato is tender, about 10 minutes.
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15
Meanwhile, in a small bowl, whisk the heavy cream until soft peaks form.
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16
Pass the potato through a ricer into a medium bowl.
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17
Fold the whipped cream into the potato and season with salt.
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18
Ladle the hot soup into warmed shallow bowls.
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19
Drizzle 8 drops of balsamic vinegar over each soup, then mound 2 tablespoons of the whipped potato in the center.
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20
Sprinkle with cayenne and serve at once.