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1
Remove chicken from refrigerator 2 hours before grilling; pat dry. Season all over with 1 tsp. each salt and pepper.
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2
With a mortar and pestle, pound garlic to a smooth puree. Add 1/2 cup oregano and pound to a coarse paste. Drizzle in just enough oil to make a thick paste, about 1 tbsp. (Or, mince garlic, then mash with the flat side of a chef's knife. Mince oregano and blend with mashed garlic and oil.) Rub paste all over chicken pieces (anytime after seasoning step).
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3
Ignite a heaping chimney of mesquite hardwood charcoal on firegrate of a charcoal grill. When fully lit but not quite glowing, about 15 minutes, spread about 1 in. thick over most of firegrate, but sloping up toward one side; the high part will be your hot area. Add about a half-chimney of unlit fruitwood chunks evenly to charcoal. Set cooking grate in place. When flames have burned down to low flickers, 5 to 8 minutes, you are ready to cook.
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4
Meanwhile, remove stems but not seeds from chiles. In a clean coffee grinder, grind chiles to a coarse powder. Finely chop remaining 1/2 cup oregano and mix in a bowl with chiles. Mash in butter, plus pepper and salt to taste.
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5
Grill corn in husks over hot part of fire, turning often, until blackened all over, 10 to 12 minutes; set aside. Light another chimney of charcoal in a heatproof area and let burn until glowing.
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6
When grill temperature is down to medium (about 400u00b0), scrub cooking grate with a grill brush, then wipe grate with a clean, dry rag to remove soot. Arrange chicken over cooler part of fire, skin side down and with thickest part nearest hot area. Set a couple of plates on chicken to flatten and help it crisp. Grill, uncovered, until well browned underneath, 10 to 12 minutes.
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7
Meanwhile, prep lettuces: Quarter each head lengthwise through core. Brush with remaining 1 tbsp. oil and season lightly with salt.
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8
Husk corn and remove any silk by rubbing ears with a kitchen towel. Rub sparingly all over with chile butter (about 1 tsp. per ear; dripping butter will cause flare-ups).
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9
When chicken is browned, remove plates and turn pieces over. Through hinged flap of cooking grate, add several more coals from second chim-ney to replenish fire (keep heat at medium). Cook chicken, covered, until an instant-read thermo-meter inserted through thickest part reads 155u00b0, 15 to 20 minutes more. Transfer to a cutting board.
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10
Add corn to grill and cook over medium-high heat (450u00b0; you may need to add a few more coals or wood chunks), covered and turning often, until charred in spots, 5 minutes. Remove from heat, cut into thirds, and rub with more chile butter while still hot. Put in a serving bowl.
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11
Grill lettuces on both cut sides over medium-high heat until grill marks appear, about 10 minutes total. Arrange on a platter.
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12
Carve breastbone and ribs from each piece of chicken (leave drumette attached). Set chicken on top of lettuces and serve with corn and remaining chile butter on the side.
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13
*Order from your butcher, or follow this method for carving the breasts from 2 whole chickens:
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14
Cut the first two joints off each chicken wing, leaving only the drumettes.
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15
Cut the leg quarters off, leaving as much skin intact as possible over the breast.
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16
Use kitchen shears to cut out the backbone and neck, following the chicken's natural fat line.
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17
Score down the center of the breastbone with the point of your knife, then cut in half through the bone.
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18
After grilling, slice away the breastbone and ribs.
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19
Make ahead: Up to 1 day, season chicken; chill.
