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1
Put 1 cup flour with salt and pepper in a large (1-gallon) sealable plastic bag, then seal bag and shake to combine.
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2
Turn chicken pieces in milk in a bowl, then add chicken to flour mixture and seal bag (discard milk).
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3
Shake to coat and let stand in bag while oil heats.
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4
Heat oil in skillet over moderately high heat until it registers 360F on thermometer (see cooks' note, below).
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5
Add chicken, skin sides down, and cook, covered, until golden, about 5 minutes.
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6
Turn chicken over with tongs and cook, covered, 5 minutes more.
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7
Transfer chicken with tongs to a plate.
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8
Pour fat from skillet into a heatproof bowl (to cool before discarding) and add 1/2 cup water to skillet.
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9
Return chicken to skillet, skin sides up, and cook, covered, over moderate heat, turning over twice, until chicken is cooked through, about 15 minutes.
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10
Transfer chicken to a platter and cover loosely with foil to keep warm.
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11
Pour off and discard all but 1 tablespoon fat from skillet, then stir 1 tablespoon flour into remaining fat and cook over moderate heat, whisking, 2 minutes.
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12
Add 1/2 cup water and cook, scraping up brown bits, 2 minutes.
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13
Add half-and-half, whisking, and bring to a boil.
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14
Reduce heat and simmer, whisking occasionally, until sauce is thick and creamy, about 4 minutes.
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15
Season with salt and pepper and spoon over chicken.
