To Butterfly a Chicken: With heavy shears or a cleaver, cut down close to the backbone on each side, and remove the bone.
Spread the chicken open, skin side up, and pound on the breast with your fist to flatten the chicken. Cut off and discard the little nubbins at the wing elbows, and fold the wings akimbo. To hold the legs in place, make 1-inch slits in the skin on each side of the lower breast and tuck the drumstick ends through the slits.
Preheat the broiler to high.
hicken all over with butter and oil and arrange it skin side down in a shallow pan.
Set it under the broiler so the chicken surface is about 6 inches from the heat source. Let broil for about 5 minutes, then baste rapidly with the butter and oil, and continue for another 5 minutes. The surface should be browning nicely; if not, adjust the heat or the distance of chicken from broiler. Baste again, this time with the juices accumulated in the pan, and broil another 5 minutes. Then season with salt and pepper, turn the chicken skin side up, and season the surface. Continue broiling and basting with the pan juices every 5 minutes for another 10 to 15 minutes, until the chicken is done Remove the chicken to a carving board and let it rest for 5 minutes.
Meanwhile, make the deglazing sauce by first spooning cooking fat off the juices in the pan.
Then stir the shallot into the pan and simmer for a minute or so on top of the stove, until the juices are syrupy.
Swirl in the enrichment butter, pour over the chicken, and serve.
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