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 about 10 minutes, stirring occasionally, until apples are tender.
02 - Using a potato masher or immersion blender, gently mash the apples, leaving some small chunks for texture.
03 - Add granulated sugar, brown sugar, ground cinnamon, ground nutmeg, ground allspice, and salt. Stir well to dissolve sugars completely.
04 - Stir in the unsalted butter. Continue to cook over medium heat, stirring frequently to avoid scorching, until the mixture thickens and develops a golden caramel hue, about 20 to 25 minutes.
05 - Bring the mixture to a full boil. Add liquid pectin, stir thoroughly, and boil hard for 1 to 2 minutes. Remove from heat.
06 - Skim foam if necessary. Ladle hot jam 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 as needed.
07 - Allow jars to cool undisturbed. Store sealed jars in a cool, dark place. Refrigerate after opening.