Step 1
Peel core and chop apples; set apple chunks aside reserving peels and cores. Combine peels cores and 2 cups apple cider in a saucepan and bring to a boil. Reduce heat to low cover and simmer 30 minutes.
Step 2
Meanwhile combine chopped apples sugar remaining cider and cinnamon stick in a large non-aluminum saucepan and bring to a boil. Reduce heat to low. Cover and simmer stirring occasionally until apples begin to fall apart 20 to 40 minutes.
Step 3
Press peel-core mixture through a food mill or sieve placed over a bowl to catch juice. Reserve juice and discard peels and cores. Add juice to cooked apples in the saucepan and return mixture to a boil. Reduce heat and simmer uncovered and stirring occasionally until thick 40 to 60 minutes. Remove and discard cinnamon stick. Stir in pumpkin.
Step 4
Preheat the oven to 300 degrees F (150 degrees C).
Step 5
Pour apple-pumpkin mixture into a large shallow roasting pan.
Step 6
Place roasting pan into the preheated oven leaving door slightly ajar. Bake stirring every 15 minutes until thick enough to spread 1 to 1 1/2 hours.
Step 7
Inspect 6 half-pint jars for cracks and rings for rust discarding any defective ones. Immerse in simmering water until apple-pumpkin butter is ready. Wash new unused lids and rings in warm soapy water.
Step 8
Spoon apple-pumpkin butter into sterilized jars leaving 1/2-inch head space. Wipe rims and threads clean; top with hot lids and screw bands on firmly.
Step 9
Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil cover and process for 5 minutes.
Step 9
Remove the jars from the stockpot and let rest several inches apart for 12 to 24 hours. Press the center of each lid with a finger to ensure the lid does not move up or down. Remove the rings for storage and store in a cool dark area.