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1
Peel and core apple and cut into 1/4-inch dice.
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2
Melt butter in a 12-inch heavy skillet over moderately high heat until foam subsides, then saute caraway seeds, stirring, 1 minute.
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3
Add onion and saute, stirring, until softened, about 6 minutes.
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4
Add apple and celery and saute, stirring occasionally, until crisp-tender, about 4 minutes.
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5
Remove from heat and stir in remaining stuffing ingredients.
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6
Cool stuffing completely.
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7
Preheat oven to 425F.
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8
Pat chicken dry and arrange, skinned sides down, on a work surface.
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9
Remove tender (fillet strip on side where breast bone was) from each breast half if attached and reserve for another use.
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10
Beginning at center of thicker end of breast, insert a small knife horizontally, stopping about 1 inch from opposite end.
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11
Open incision with your fingers to create a 1-inch-wide pocket.
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12
Pack one sixth of stuffing into each pocket.
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13
Pat chicken dry and season with salt.
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14
Heat oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking, then brown chicken in 2 batches, about 2 minutes on each side, transferring to a small roasting pan as browned (reserve skillet).
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15
Roast chicken in middle of oven until just cooked through, 14 to 16 minutes.
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16
While chicken is roasting, stir flour into fat remaining in skillet and cook roux over moderately low heat, stirring, 1 minute.
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17
Whisk in cider and broth and bring to a boil, whisking, then boil, whisking occasionally, until thickened and reduced to about 1 cup, about 8 minutes.
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18
Let chicken stand 5 minutes, then cut each breast half diagonally into thirds.
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19
Add any juices from roasting pan and salt and pepper to taste to sauce and spoon over chicken.