Add apple cores to a large pot with 4 cups water and cinnamon sticks, if using. Simmer over medium-low heat for 1 hour, stirring and pressing down on cores with a wooden spoon occasionally. Strain out cores using a fine-mesh strainer, and return the liquid to the pot. Reduce by half over low heat, 15–20 minutes, and add honey. Stir to dissolve, and cook for an additional 5–10 minutes. Remove from heat, and let cool completely. Store in the fridge in airtight jars for up to 2 weeks.