01 - In a large, heavy-bottomed pot, combine chopped apples, lemon juice, apple cider, and water. Bring to a simmer over medium heat. Cook for 10 minutes, stirring occasionally, until apples are tender.
02 - Gently mash apples using a potato masher or immersion blender, leaving some small pieces for texture.
03 - Add granulated sugar, brown sugar, cinnamon, nutmeg, allspice, and salt. Stir thoroughly to dissolve sugars.
04 - Stir in cubed butter. Continue cooking over medium heat, stirring frequently, until mixture thickens and develops a caramel color, about 20 to 25 minutes. Stir consistently and scrape bottom to prevent scorching.
05 - Bring mixture to a full boil. Add liquid pectin, stir well, and boil rapidly for 1 to 2 minutes. Remove from heat.
06 - If needed, skim foam from surface. Spoon hot mixture into sterilized jars, leaving 1/4-inch headspace. Wipe rims, apply lids, and process in a boiling water bath for 10 minutes, adjusting for altitude if required.
07 - Allow jars to cool undisturbed. Store in a cool, dark area. Keep refrigerated after opening.