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1. Toast peppercorns in a large flat-bottomed carbon-steel wok or heavy skillet over high heat until fragrant, about 1 minute. Crush in a mortar and pestle or with a rolling pin. Set aside near the stove.
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2. Meanwhile, combine broth, soy sauce, rice vinegar, rice wine (or sherry), sesame oil, honey (or sugar) and star anise in a medium bowl. Finely chop enough scallions to equal 2 tablespoons and reserve for garnish; cut the remaining scallions into 2-inch lengths. Place the sauce and scallion pieces near the stove.
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3. Heat canola oil in the wok (or skillet) over high heat until shimmering. Reduce heat to medium-high; add 2 drumsticks and 2 thighs and cook, undisturbed, for 4 minutes. Carefully flip the chicken over and cook for 3 minutes on the other side, reducing the heat as needed if the pan gets too hot. Transfer the chicken to a plate and repeat with remaining chicken; remove to the plate. Add the scallion pieces, garlic and ginger to the pan; cook, stirring once or twice, until they begin to brown, about 1 minute. Add the crushed peppercorns and stir for 5 seconds. Add the reserved sauce and cook 2 minutes. Add the chicken; stir to coat with the sauce.
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4. Adjust the heat to maintain a simmer, cover the pan and cook, turning the chicken halfway through, until an instant-read thermometer inserted into the thickest part without touching bone registers 165u00b0F, 15 to 20 minutes. Stir in basil leaves and cook, uncovered, for 1 minute more. Garnish with the chopped scallions and chopped basil.
