In a 10-inch skillet over medium, heat the oil until shimmering. Add the ginger and scallion whites, then cook, stirring, until the scallions begin to brown, about 2 minutes. Add the star anise and cook, stirring, until fragrant, about 30 seconds.

Stir in ¾ cup water, bring to a simmer over medium-high and cook until the ginger begins to soften, about 3 minutes. Remove from the heat and whisk in the soy sauce, molasses and ½ teaspoon pepper. Cool to room temperature, about 30 minutes.

Set a fine mesh strainer over a liquid measuring cup, then pour mixture into the strainer until you have ½ cup strained; cover and refrigerate until needed. Transfer the remaining mixture to a large bowl and add the solids in the strainer.

Using a sharp knife, cut 2 parallel slashes across the skin side of each thigh, slicing all the way to the bone. Add the chicken, skin side down, to the soy mixture in the bowl and push the pieces down to submerge. Cover and refrigerate for 1 to 2 hours.

Heat the oven to 375°F with a rack in the middle position. Line a rimmed baking sheet with foil. Set a wire rack on top and mist with cooking spray.

Remove the chicken from the marinade, allowing any excess to drip off and scraping off any solid bits, then arrange skin side up on the prepared rack, making sure the skin on each piece lays flat.

Roast until the skin is mahogany brown and thickest part of the thigh reaches 175°F, about 45 minutes. Let rest on the rack for about 10 minutes. Meanwhile, stir the reserved marinade to recombine, then stir in the sesame oil and 2 tablespoons of scallion greens.

Transfer the chicken to a platter and sprinkle with the remaining scallion greens. Serve with the sauce.