01 - In a large, heavy-bottomed pot, combine the 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 - Gently mash the apples using a potato masher or immersion blender, keeping some small apple pieces for texture.
03 - Add the granulated sugar, brown sugar, cinnamon, nutmeg, allspice, and salt. Stir well until the sugars are fully dissolved.
04 - Stir in the cubed butter. Continue cooking over medium heat, stirring frequently, until the mixture thickens and attains a golden caramel color, about 20 to 25 minutes. Stir gently to prevent scorching.
05 - Bring the mixture to a rolling boil. Add the liquid pectin, stir thoroughly, and boil vigorously for 1 to 2 minutes. Remove from heat.
06 - Skim off any foam, then ladle the hot jam into sterilized jars, allowing 1/4-inch headspace. Wipe jar rims, secure lids, and process in a boiling water bath for 10 minutes, making altitude adjustments as needed.
07 - Allow jars to cool completely at room temperature. Store in a cool, dark environment. Refrigerate after opening.