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Step 1
Dissolve salt in 2 quarts cold water in largecontainer. Submerge chicken in brine, cover, andrefrigerate for 30 minutes to 1 hour. Remove chickenfrom brine and pat dry with paper towels.
Step 2
Adjust oven rack to lower-middle positionand heat oven to 475 degrees. Heat oil in ovensafe12-inch skillet over medium-high heat until justsmoking. Place chicken skin side down in skilletand cook until skin is well browned and crisp, 8 to10 minutes. Transfer breasts to large plate. Flipthighs and legs and continue to cook until brownedon second side, 3 to 5 minutes longer. Transferthighs and legs to plate with breasts.
Step 3
Pour off and discard fat in skillet. Return skilletto medium heat; add butter, shallot, and garlic andcook until fragrant, 30 seconds. Sprinkle flour evenlyover shallot-garlic mixture and cook, stirring constantly,until flour is lightly browned, about 1 minute.Slowly stir in broth and lemon juice, scraping up anybrowned bits, and bring to simmer. Cook until sauceis slightly reduced and thickened, 2 to 3 minutes. Stirin 1 tablespoon zest and remove skillet from heat.Return chicken, skin side up (skin should be abovesurface of liquid), and any accumulated juices to skilletand transfer to oven. Cook, uncovered, until breastsregister 160 degrees and thighs and legs register175 degrees, 10 to 12 minutes.
Step 4
While chicken cooks, chop parsley, oregano,and remaining 1 teaspoon zest together until finelyminced and well combined. Remove skillet fromoven and let chicken stand for 5 minutes.
Step 5
Transfer chicken to serving platter. Whisksauce, incorporating any browned bits from sidesof pan, until smooth and homogeneous, about30 seconds. Whisk half of herb-zest mixture intosauce and sprinkle remaining half over chicken. Poursome sauce around chicken. Serve, passing remainingsauce separately.