Don’t be put off by the sugar in this recipe—it’s balanced by the vinegar and soy sauce.
Heat oil in a large wide heavy pot over medium-high heat. Season chicken with salt and, working in 2 batches, cook until golden brown and crisp, 6–8 minutes per side; transfer to a plate. Add garlic to pot and cook, stirring often, until golden, about 2 minutes; transfer to plate with chicken. Pour off fat from pot.
Return pot to medium-high heat and add 1/2 cup water, scraping up browned bits. Add brown sugar; stir to dissolve, then cook, stirring, until mixture thickens and turns a deep amber color, about 4 minutes. Carefully add vinegar (it may bubble up; sugar will crystallize); stir to dissolve sugar.
Add ginger, broth, and soy sauce, then add chicken, skin side up, and garlic. Bring to a boil, reduce heat, and simmer gently until chicken is cooked through, 20–25 minutes. Transfer chicken to a plate.
Bring cooking liquid to a boil and cook until thick enough to coat a spoon, about 10 minutes. Return chicken to pot; turn to coat. Top with scallions and serve with rice.
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