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1
To make the rich broth, in a large pot, combine the chicken parts, onion, carrot, celery, parsley, thyme, broth, and water as needed to cover the chicken and bring to a boil over medium-high heat.
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2
Decrease the heat to maintain a gentle simmer, cover partially, and cook until the meat is falling off the bones and the broth is well colored, about 2 hours.
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3
Remove from the heat, let cool to room temperature, and strain through a fine-mesh sieve.
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4
Discard the contents of the sieve and refrigerate the broth until the fat congeals across the top, at least 2 hours, or preferably overnight.
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5
To make the meatballs, crack the eggs into a medium bowl and whisk to mix.
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6
Add the butter, matzo meal, chicken, and salt and knead with your hands until thoroughly blended.
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7
Cover and refrigerate for at least 1 hour or up to overnight.
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8
To make the soup, skim the fat off the broth.
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9
Pour the broth into a large pot and bring to a boil over medium-high heat.
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10
With moist hands, form the chicken mixture into 1 1/4-inch balls and drop them into the boiling broth as you go.
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11
Decrease the heat to maintain a brisk simmer, cover, and cook until the meatballs rise to the top and are tender all the way through, about 30 minutes.
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12
To serve, ladle the broth and balls into large individual bowls and garnish each bowl with scallion and parsley.
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13
Serve piping hot.