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1
Pat chicken dry and sprinkle inside and out with salt and pepper.
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2
Stuff cavity with thyme and chill chicken, loosely covered, at least 3 hours (to allow seasoning to permeate meat).
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3
Transfer chicken to a 7- to 8-quart heavy pot, then add stock, water, onion, garlic, celery rib, and bay leaf and bring to a boil.
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4
Reduce heat and gently simmer chicken, covered, until juices run clear when a thigh is pierced with a skewer and thermometer inserted into thickest part of a thigh (do not touch bone) registers 170F, about 45 minutes.
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5
Transfer chicken to a large platter and let stand, loosely covered with foil, 20 minutes.
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6
Reserve cooking liquid in pot, uncovered, and discard onion, celery, garlic, and bay leaf.
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7
Starting about 1/2 inch from root end, make a lengthwise cut through middle of each leek (keep leek intact).
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8
Wash leeks well under cold running water and drain.
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9
Halve potatoes.
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10
Bring chicken cooking liquid to a boil, then add leeks, potatoes, carrots, parsnips, and celery root and simmer, partially covered, until tender, about 20 minutes.
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11
Carefully transfer vegetables with a slotted spoon to platter with chicken and keep warm, loosely covered with foil.
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12
(Reserve cooking liquid for another use if desired cool, uncovered, then chill, covered.)
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13
Mash garlic and capers to a paste with salt using a mortar and pestle (or mince and mash with a large heavy knife).
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14
Transfer to a food processor and pulse with parsley and watercress until herbs are finely chopped.
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15
With motor running, add oil in a slow stream and process until smooth.
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16
Season sauce with salt and pepper.
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17
Serve chicken and vegetables with sauce.
