Prep apples. Wash apples, then peel and core them (or leave peels on if you’ll run the finished sauce through a food mill). Slice and measure 12 cups sliced apples (about 3 lb prepared).
Cook the fruit. Add apples and 2 cups pomegranate juice to a large, heavy-bottomed pot. Bring to a gentle boil, then reduce to a steady simmer. Cook, stirring often, until the apples are completely soft and collapsing, about 15–25 minutes. If the pot starts to stick, lower the heat and stir more frequently.
Purée smooth. Purée the hot mixture to your preferred texture. A food mill gives the smoothest applesauce (and removes peels neatly), but an immersion blender works too. For canning, make sure it’s a true purée with no large chunks so heat penetrates evenly.
Reheat before filling jars. Return the purée to the pot and bring it back to a full boil, stirring so it doesn’t scorch. Keep it hot while you fill jars.
Fill jars. Ladle the boiling-hot sauce into hot pint jars, leaving 1/2-inch headspace. Remove air bubbles, adjust headspace if needed, wipe rims, and apply lids and rings to fingertip tight.
Process. Process in a boiling-water canner for 15 minutes for pints or 20 minutes for quarts, adjusting for altitude (see notes).
Cool and check seals. Turn off heat, remove canner lid, and let jars rest 5 minutes. Remove jars and cool undisturbed 12–24 hours. Check seals, label, and store.