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1
In a large saucepan, combine chicken with carrot, celery, leek, tarragon sprigs, wine, salt, and peppercorns. Add enough water to cover chicken and other ingredients by about 1 inch. Set over medium-high heat until water temperature reaches between 150 and 160u00b0F (66 and 71u00b0C) on an instant-read thermometer; adjust heat to maintain water temperature in the 150-160u00b0F range. It's okay if the temperature bounces around a little, but try to keep it above 150 and below 170u00b0F (77u00b0C). Cook until thickest part of chicken registers 150u00b0F (66u00b0C) on an instant-read thermometer, about 1 hour. Remove chicken from broth and let rest.
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2
When chicken is cool enough to handle, remove skin and bones. (If you want, return skin and bones to poaching liquid and simmer for 30 minutes longer, then strain and reserve liquid as a broth for another use.) Cover chicken breasts with plastic wrap, pressing plastic directly and firmly against the surface of the meat, and set aside.
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3
Fill a skillet large enough to accommodate asparagus with cold water, add a large pinch of salt, then bring to a boil over medium-high heat. Add asparagus and cook until tender, about 4 minutes. Transfer asparagus to a paper towel-lined plate to drain, then discard paper towels. Drizzle asparagus with melted butter and set aside.
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4
Using a blender or food processor, puree mayonnaise, sour cream, vinegar, watercress, tarragon, parsley, chives, and anchovies until smooth. Season with salt and a generous grinding of black pepper. Dressing will keep, covered, in the refrigerator for up to 1 week.
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5
About 1 hour before serving, allow dressing to come to room temperature. Before serving, use a whisk or electric mixer to whip cream in a large metal bowl until soft peaks form. Fold whipped cream into dressing to suit your taste.
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6
Slice warm or room-temperature chicken breasts against the grain. Spoon some sauce onto a large platter. Arrange chicken on top of sauce and arrange warm or room-temperature buttered asparagus around chicken. Spoon more sauce over chicken. Season with salt and pepper and garnish with minced fresh chives. If you prefer, you can also serve on individual plates. Serve any extra green goddess sauce on the side.
