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1
Melt the butter in a large pot over medium-high heat.
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2
When the butter begins to bubble, add the shallots, celery, mushrooms, carrots, and a pinch of salt, and cook until the vegetables are starting to soften, about 5 minutes.
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3
Add the flour, and cook, stirring frequently, until the vegetables are coated, about 2 minutes.
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4
Gradually stir in the chicken stock.
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5
Bring the soup to a simmer, stirring frequently, and cook until the vegetables are tender and the soup has thickened slightly, about 15 minutes.
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6
Meanwhile, bring a large pot of water to a boil.
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7
Generously salt the water, and cook the egg noodles until they are just tender, about 7 minutes (this will vary from brand to brand, so check the bag for an accurate cooking time).
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8
Drain the noodles in a colander, transfer them to a bowl, toss them with the vegetable oil to prevent sticking, and set them aside.
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9
Add the chicken slices to the soup pot, and simmer until the chicken is cooked through, 4 to 5 minutes.
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10
Add the half-and-half.
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11
Stir in the reserved noodles, the peas, and the parsley or dill, and simmer for another 5 minutes, until heated through.
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12
Season with salt and plenty of black pepper.
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13
This soup can be prepared a day in advance (just allow the dish to cool slightly after cooking, then cover and refrigerate).