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1
In a medium saucepan of boiling water, blanch the parsley leaves until tender but still bright green, about 3 minutes.
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2
Drain well.
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3
Transfer the parsley to a food processor and puree.
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4
Scrape the puree into a bowl.
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5
Clean out the food processor.
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6
Add the white mushrooms to the food processor and pulse to mince.
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7
In a large nonstick skillet, heat the oil.
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8
Add the minced mushrooms, season with salt and pepper and cook over high heat until the liquid has evaporated, about 5 minutes.
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9
Add the water and stir to scrape up any browned bits.
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10
Add the cream, cover and simmer over low heat for 10 minutes.
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11
Strain the mushroom cream through a fine strainer into a small saucepan, pressing on the solids.
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12
Simmer the cream over moderately high heat until reduced to 1/3 cup, about 2 minutes.
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13
Season with salt.
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14
In a large skillet, melt the butter.
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15
Add the shallot and cook over moderately high heat until softened, 2 minutes.
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16
Add the chanterelles, season with salt and pepper and cook over moderate heat, stirring occasionally, until browned, 10 minutes.
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17
Set a round rack in a large, wide pot.
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18
Add enough water to reach just under the rack without touching it.
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19
Cover the pot and bring the water to a boil.
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20
Butter four 1 1/4-cup heatproof porcelain bowls, about 4 1/2 inches wide at the top tapering down to 2 inches wide at the bottom.
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21
Alternatively, use ramekins.
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22
Spoon the parsley puree into the bowls.
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23
Crack 1 egg into one of the porcelain bowls; season with salt and pepper.
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24
Repeat with the remaining eggs.
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25
Cover each bowl with plastic wrap.
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26
Carefully set on the rack in the pot, cover and steam over low heat until the whites are firm and the yolks are runny, about 12 minutes.
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27
Discard the plastic wrap.
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28
Reheat the mushroom cream and chanterelles.
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29
Spoon the cream over the eggs, top with the chanterelles and serve.