In the large roasting pan, toss the apples with the cider and maple syrup, then lay the cinnamon sticks around in the apples. Roast until the apples are very soft and mash easily, 30 to 45 minutes.
Remove the cinnamon sticks. If you left the peels on, mash the apples slightly with a potato masher, then run them through the food mill. Use the fine blade for apple butter and the coarse blade for apple sauce. If you peeled the apples before roasting, then process the cooked apples in a food processor. Applesauce is finished, just set aside to cool, then put into containers and refrigerate or freeze. You can also keep a cup or two of applesauce and turn the rest of the mixture into apple butter, just make sure that the mixture is finely ground so that you get that nice, smooth texture for which apple butter is famous.
Step 2 - Apple Butter
Reduce oven temperature to 300° F/150° C. Stir the milled apples with any remaining liquid from the roasting pan and the ground cinnamon, cloves, and allspice. Add more maple syrup if desired.
Spread the mixture into the roasting pan, making sure to spread evenly throughout the pan. Cook in the oven for 1 to 1-½ hours, depending on how much you started with. Stir every 30 minutes, working the edges into the middle. Test for doneness by dropping a spoonful onto a plate. If no liquid is released, then the apple butter is ready.
Remove from oven and allow to cool completely. Spoon into containers and refrigerate or freeze.
To can the apple butter, prepare the jars according the directions for boiling water canning. Skip step 6 above (cooling) and add the hot apple butter to the hot jars, leaving ¼-inch (0.5 cm) head space. Remove the air bubbles and adjust the air space by adding more butter if necessary. Make sure head space is precisely ¼-inch (0.5 cm), or the jars will not seal properly. Wipe the rim clean and center the lid on the jar. Screw the band on just until finger tight. Do not over tighten.
Process jars according to the boiling water canning directions for 10 minutes with the lid on. Remove the canner lid and wait 5 more minutes, then remove the jars. Allow them to cool completely, then store in a dark location for up to one year.
NotesBoth applesauce and apple butter will keep in the refrigerator for up to 2 weeks, or several months in the freezer.For freezing, I like the Ball® Plastic (8 ounce/16 ounce) Freezer Jars. They are just the right size and they stack easily.VariationsOther fruits to try with apples: pears, plums, apricots, peaches, cranberries.Other spices to use: star anise, ground ginger, ground cardamom