Place the apples in a large heavy-bottom pot. Add the apple cider, then partially cover with a lid and place the pot over medium heat. After 15 minutes, use a sturdy wooden spoon to stir up the softened apples at the bottom. After 15 more minutes, reduce the heat to medium-low and stir again. Continue to cook on medium-low for another 45 minutes, stirring occasionally.
Remove from heat and give the fruit one final big stir. Place a fine-mesh sieve over the bowl of your slow-cooker and, working in batches, press the cooked fruit through the sieve with the back of a ladle. Discard the solids. Stir in the maple syrup. Turn the slow cooker onto low, cover with the lid, and set for 8 hours. Once the butter begins to bubble, crack the lid open slightly so the steam can evaporate. This helps the fruit butter to reduce. Keep the lid slightly cracked, and stir occasionally.
Transfer to clean jars, and cool completely overnight in the refrigerator. Cover with lids and rings. Label with the date and freeze. Apple butter will keep for up to 1 week in the fridge or 3 months in the freezer.