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1
Cut out backbone from chicken with kitchen shears and discard. Pat chicken dry, then spread flat, skin side up, on a cutting board. Cut a 1/2-inch slit on each side of chicken in center of triangle of skin between thighs and breast (near drumstick), then tuck bottom knob of each drumstick through slit. Tuck wing tips under breast. Sprinkle chicken all over with salt and ground pepper.
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2
Heat 3 tablespoons butter in 10-inch cast-iron or heavy nonstick skillet over moderate heat until foam subsides. Add chicken, skin side down, and arrange larger rosemary sprigs over chicken. Cover with parchment round and second skillet, then top with weights. Cook chicken until skin is browned, about 15 minutes. Remove and reserve weights, top skillet, parchment, and rosemary, then carefully loosen chicken from skillet with a spatula. Turn chicken over and re-place rosemary sprigs, then re-cover with parchment, skillet, and weights. Cook until chicken is just cooked through, 15 to 20 minutes more.
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3
Toast peppercorns in a dry 1-quart heavy saucepan over moderate heat, shaking pan occasionally, until fragrant, about 3 minutes. Transfer to a clean cutting board and coarsely crush with a rolling pin. Return peppercorns to saucepan and bring to a simmer with syrup, 1/2 cup broth, and small rosemary sprig, then reduce heat and simmer 20 minutes.
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4
Transfer chicken to a platter and loosely cover with foil. Add vinegar to skillet and deglaze, boiling and scraping up brown bits with a wooden spoon until liquid is reduced by half. Stir in maple mixture and remaining 1/4 cup broth and boil until slightly syrupy, about 3 minutes. Reduce heat to low and swirl in remaining 2 tablespoons butter. Season sauce with salt and pour through a fine-mesh sieve into a bowl, discarding solids. Serve chicken with sauce.
