To Make the Dough: Within the bowl of a meals processor, course of flour and salt collectively till mixed, about 3 seconds. Add butter and pulse till dimension of huge peas, about six to eight 1-second pulses.
In small bowl, combine bitter cream and 4 tablespoons ice water till mixed. Add half of bitter cream combination to flour combination and pulse for 3 1-second pulses. Repeat with remaining bitter cream combination. Pinch dough with fingers; if dough is floury, dry, and doesn’t maintain collectively, add 1 to 2 further tablespoons water and course of till dough kinds giant clumps and no dry flour stays, three to 5 1-second pulses.
Flip dough onto work floor and form into ball. Flatten right into a 5-inch disk and wrap in plastic. Refrigerate till agency however not onerous, 1 to 2 hours. (Dough could be refrigerated in a single day.)
To Roast the Rooster and Greens: Warmth oven to 450 levels. In heavy-bottomed 12-inch ovenproof skillet, warmth oil over medium-high warmth it simply begins to smoke; swirling to coat evenly with oil. Brown rooster items pores and skin aspect down till deep golden, 3 to 4 minutes; flip rooster items and brown till golden on second aspect, 3 to 4 minutes longer. Switch rooster to giant plate; drain all however 1 tablespoon fats.
Set skillet over medium warmth. Add pearl onions and prepare dinner, stirring often, till browned, about 3 minutes. Enhance warmth to medium-high and add onion, carrots, celery, and salt and pepper to style; prepare dinner, stirring often, till greens start to brown, 2 to three minutes. Return rooster items to skillet pores and skin aspect up and place in oven. Roast till thickest a part of breast registers about 160 levels on instant-read thermometer and thickest a part of thigh and drumstick registers about 175 levels, 18 to 25 minutes. Utilizing an oven mitt, take away skillet from oven. Switch rooster to platter and let relaxation 1 hour. Set skillet with greens apart.
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