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1
Preheat oven to 425u00b0. Very thinly slice half of lemon; discard any seeds. Cut remaining lemon half into 2 wedges. Season chicken thighs with salt and pepper.
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2
Heat 1 tsp. oil in a large ovenproof skillet ovher medium heat and cook chicken (keeping thighs folded) until halfway cooked, about 10 minutes.
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3
Scatter half of lemon slices over chicken and half on bottom of skillet (the slices on top of the chicken will soften; those in the skillet will caramelize). Transfer skillet to oven and roast until chicken is cooked through and lemon slices on bottom of skillet are caramelized, 6-8 minutes.
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4
Transfer chicken pieces and caramelized lemon slices to a warm platter. (Leave softened lemon slices in the skillet.) Return skillet to medium heat. Add oregano sprigs, shallot, garlic, and red pepper flakes; cook, stirring frequently, until fragrant, about 1 minute.
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5
Remove skillet from heat. Add wine; cook over medium heat until reduced by half, 1-2 minutes. Add broth; cook until thickened, about 3 minutes. Squeeze 1 lemon wedge over and season sauce with salt, pepper, and juice from remaining lemon wedge, if desired. Drizzle with 2 tsp. oil. Return chicken to skillet to rewarm. Serve topped with caramelized lemon slices.