Use the largest stock pot you have. Use multiple pots if needed. Put just enough water in the pot to cover the bottom 1/4" to 1/2" deep. Approximately 1/4 to 1/2 cup of water, depending on the size of your pot.
Peel and core apples, then cut them into quarters.
Cook on medium-high heat until the pot comes to a boil. Turn the heat down to a high simmer. Stir on occasion.
When the apples are beginning to get close to your desired consistency, sweeten and season your applesauce. This is a general guideline, season to your taste, start small, you can always add more. For a half bushel of apples, I suggest adding 1 to 1½ cups of sugar and 1½ tablespoons of ground cinnamon.
Continue cooking the apples until you reach your desired consistency. Depending on your choice of apples, this could take as little as 30 minutes to 2 hours. Taste the applesauce, add more sugar or cinnamon as needed.
When the applesauce is almost done, prepare the canner and jars to process applesauce in the boiling water canner. I prefer to sterilize my jars before canning, even though the processing time of this recipe is sufficient to skip sterilization. You do what's right for you!
Fill hot jars with hot applesauce, leaving 1/2 inch headspace.
Use a bubble tool to stir the applesauce and remove any air bubbles. Clean the jar rim with a vinegar-soaked washcloth or paper towel.
Add your choice of canning lid, a metal one-use lid, or a reusable Harvest Guard canning lid. Tightening the ring finger tight.
Place filled jars into the rack of the hot water bath canner using a jar lifter. Bring water back to a boil, submerge the jars in the water with at least 1 to 2 inches of water above the jars.
Process pint jars for 15 minutes, quart jars for 20 minutes. Make adjustments based on your altitude if necessary. (see Notes below)
Once the processing time has passed, turn off the heat and pull the rack out of the water. Allow the jars to acclimate to room temperature for at least 5 minutes prior to removing jars from the water bath canner.
Cool the jars for 24 hours, remove rings, and check lid seals. Store jars of applesauce in a cool, dry place.