In a small saucepan, bring apple peels, brown sugar, and ½ cup water to a boil over medium-high heat. Cook, stirring constantly, until sugar is dissolved, about 1 minute. Reduce heat to low; cook, stirring occasionally, until slightly thickened, about 5 minutes. Remove from heat; let stand for 15 minutes. Drain, discarding apple peels. Cover and refrigerate for up to 1 month.