Blushing Applesauce

Place apples in a large pot with the sugar, water, and lemon juice. Bring to a boil, then reduce heat to medium-low and simmer uncovered, stirring occasionally, until the apples are very soft and lose their shape, about 25 minutes. Remove the apples from the heat and allow to cool slightly. Puree apples in a food processor or food mill. If using the food processor, strain the apples through a sieve to remove the pieces of apple skin. Stir in the cinnamon and nutmeg. Serve at room temperature or refrigerate and serve cold.