Place the peeled, cored, and chopped apples in a large pot.
Add the water, white sugar, and ground cinnamon.
If using a cinnamon stick instead of ground cinnamon, add it to the pot at this stage.
Stir the ingredients until evenly combined.
Cover the pot with a lid.
Place the pot over medium-high heat and bring the mixture to a boil.
Once boiling, reduce the heat to low.
Simmer the apples for 20 to 30 minutes, or until they are very soft and tender.
Stir occasionally during cooking to prevent sticking and to help the apples cook evenly.
Remove the pot from the heat.
If a cinnamon stick was used, remove and discard it.
Using a potato masher or fork, mash the apples until the applesauce reaches the desired consistency.
For a chunky applesauce, mash lightly.
For a smoother applesauce, continue mashing until the texture is soft and even.
Taste and adjust with additional cinnamon or sugar, if desired.
Serve warm, or allow the applesauce to cool before storing.