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1
In a large saucepan, heat the schmaltz over medium-high heat.
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2
Add the onion and an aggressive four-finger pinch of salt.
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3
Stir to coat with the fat, cooking for a minute or two.
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4
Add the carrots and celery and continue to cook for 5 to 10 minutes (dont burn them; reduce the heat to medium if necessary).
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5
Add the chicken.
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6
If using raw chicken, stir and cook till the chicken has lost all its color, about 5 minutes; if using cooked chicken, just stir briefly to heat it through.
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7
Add the flour, stir to coat everything, and cook for a few more minutes.
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8
Give the meat and vegetables several grinds of pepper.
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9
Add the stock and stir continuously.
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10
Scraping the bottom of the pan with a wooden spatula, until the stock thickens (turn the heat to high until it does, if you wish).
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11
When it begins to simmer, turn the heat down and let it cook for another 10 minutes.
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12
Make the gnocchi:
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13
Combine the stock, schmaltz, and salt in a medium saucepan over high heat.
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14
When the liquid reaches a simmer, lower the heat to medium, and add the flour.Stir continuously until all the water has been absorbed and a uniform paste has formed.
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15
Continue to cook, stirring, for another minute or two.
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16
Set the pot aside to cool for 5 minutes, or hold the bottom fo the pan under cold running water to cool it enough that the eggs don't cook when you add them.
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17
Crack an egg into the pan and quickly stir it to combine (it will be slick at first, but the paste will soon embrace the egg).
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18
Repeat with the remaining eggs (4 is standard, but 5 will make it richer).
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19
Stir in herbs.
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20
Invert a large zipper-top plastic bag over your hand and use it to gather up all the pate a coux, then re-invert the bag with the choux inside.
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21
Snip 1/2 inch/25 centimeters off one corner of the gnocchi bag and pipe the dough into the pot, cutting the dumplings off in 1 1/2-inch/4-centimeter lengths.
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22
Cook until the dumplings are done, about 5 minutes.
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23
Stir in the vinegar or lemon juice and taste the liquid.
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24
If it needs more salt or pepper, add it.
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25
If it needs more acidity, add more vinegar or lemon juice.
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26
Serve, garnishing with fresh herbs if you have them.
