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Chicken and Veggies:
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Thoroughly wash the chicken inside and out, taking especial care to clean out clumps of blood in the cavities
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Reserve the giblets for another use
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If you can get the feet, clean them and add them to the pot; they add a wonderful richness to the broth
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Put the cheesecloth bundle into the cavity along with some of the garlic
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Scatter the slices of one of the carrots on the bottom of the slow cooker and put the chicken on top of it
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Put the rest of the ingredients around the pot
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Add enough water and/or dry white wine to come halfway up the sides of the pot
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Cover tightly and cook on high for at least 4 hours or medium for at least 6 hours, depending on the size of your chicken
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Meanwhile, make the lemon tarragon mayonnaise
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Lemon Tarragon Mayonnaise:
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Be sure to use French tarragon and not any other kind
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You really will notice the difference in flavor
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Place all the ingredients except the oil in a blender or food processor and whiz until smooth
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Start adding the oil a drop at a time, allowing it to emulsify
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After you have added a good soupspoonful of oil to the mixture, you can start adding it in a thin stream
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Keep adding the oil until the mayonnaise thickens enough to make a slurping noise (if using a blender, this sound does not happen in a food processor)
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Taste and adjust seasoning
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Chill until ready to use
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When the chicken is tender and done, remove it from the slow cooker and Let it rest at least 15 minutes
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If you plan to chill it, do so
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Remove the vegetables and let them cook to the extent you want, or keep warm
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Take the cheesecloth out of the cavity of the chicken and squeeze it Into the soup to get all the flavor out of ut
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Defat the broth
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Cook some super fine egg noodles to add to the soup
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Use some of the broth the braise the escarole
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Remove the chicken from the bones when it is at the temperature you want and arrange it with the vegetables on a large platter
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Depending on the size of you platter, you can also put the escarole there or on a separate one
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Nap with the lemon tarragon mayonnaise and serve the rest of the mayonnaise on the side