This smooth, spiced and not-too-sweet version of applesauce is just wonderful and the perfect accompaniment to potato pancakes. Macintosh apples make the best applesauce both, for their willingness to quickly surrender their texture and because of their rosy color, which gives the finished applesauce a beautiful pink hue. Leftover applesauce will stay great for up to three weeks in the refrigerator—although it won’t last that long!
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Place unpeeled apple wedges (including the cores) with the apple juice or cider and the cinnamon stick(s) in a 6-to 8-quart heavy-bottomed saucepan and stir. Cover and bring the mixture to a full simmer over medium-high heat. Reduce heat to low and simmer the apples until very tender, stirring and mashing frequently, 15 to 20 minutes.
Position a medium-mesh wire strainer or a food mill over a large bowl. Transfer the cooked apples, in batches, to strainer or food mill and force through into the bowl beneath, leaving the skins, cinnamon sticks and any seeds behind. (A flat-edged wooden spatula works perfectly when pushing apples through a strainer.) Discard what’s left in strainer or food-mill and repeat with the remaining cooked apples. Stir in the sugar, cinnamon, nutmeg, salt and vanilla. Cool the applesauce to room temperature, divide among jars or plastic containers and secure them with lids. The applesauce will keep perfectly for up to 3 weeks in the refrigerator.
Enjoy the applesauce chilled or slightly warmed.