Bring apple peels, brown sugar, and water to a boil in a large saucepan over medium-high heat. Boil, stirring constantly, 1 minute or until sugar is dissolved. Reduce heat to low, and cook 5 minutes or until slightly thickened. Remove from heat, and cool completely (about 1 hour). Pour mixture through a wire-mesh strainer into a large bowl; discard apple peels. Pour syrup into glass jars. Store in an airtight container in refrigerator up to 3 weeks.