In a small saucepan over low heat, combine the pears and vinegar. Cook, stirring frequently to prevent scorching, until the pears begin to break down, about 15 minutes. Remove the pan from the heat and add the brown sugar, stirring until dissolved. Add the ginger, return to low heat, and cook, stirring almost constantly, until the mixture is dark brown and very thick, about 10 minutes. Let cool to room temperature. Cover and refrigerate for up to 5 days.