Wash apples. Remove cores by cutting the apples in quarters, then cutting out the core section of each piece with an angled wedge cut. Cut apple quarters into large chunks and add to a large saucepot.
Add water and cover pot. Cook apples on high heat until boiling, then reduce to a simmer on low to medium low. Simmer until apples are soft, about 10-15 minutes. Stir occasionally to prevent possible scorching. Remove from heat.
Cool apples for a few minutes and transfer to a blender or food processor. Blend on high speed until applesauce becomes very smooth.
Cool completely and store in jars in the refrigerator for up to 1 week.
Notes
If you do not own a blender or food processor, you will need to pass the applesauce through a food mill to filter out the skins. Otherwise you will need to peel the apples.