Applesauce is so simple to make, and so versatile, that it makes store-bought versions seem pale and insipid by comparison!
Experiment with different varieties of apples to find your favorite flavor combination. Add pears or cranberries to vary the taste profile. Purée for a smooth texture, or mash with a light touch for a chunky sauce. Sweeten to your taste and play with spices like star anise, allspice, Chinese Five Spice Powder, ginger, and vanilla to develop an applesauce that's uniquely yours. The recipe here is simply a guideline and makes a smooth puréed sauce. If you prefer more texture, peel the apples before cooking.
Cut the apples into large, even chunks. Place the apples in a medium-size saucepan and add the water. Cover the pan and place over medium-high heat. Cook until the apples are very soft, 10 to 15 minutes. Watch carefully so that the apples don't scorch; it may be necessary to add a tablespoon more water or reduce the heat.
Purée the cooked apples in a food mill or press through a mesh strainer, discarding the skins. Add the sugar and spices to the warm purée and stir until dissolved.
Serve hot, warm, or cold. The applesauce can be stored in the refrigerator, covered, for up to a week, or frozen for 3 months.