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.