01 - In a large, heavy-bottomed pot, combine chopped apples, lemon juice, apple cider, and water. Bring to a simmer over medium heat and cook for 10 minutes, stirring occasionally, until apples are tender.
02 - Using a potato masher or immersion blender, lightly mash the apples to achieve a slightly chunky consistency.
03 - Add granulated sugar, brown sugar, cinnamon, nutmeg, allspice, and salt. Stir thoroughly until sugars are dissolved.
04 - Stir in unsalted butter. Cook over medium heat, stirring frequently and scraping the bottom, until the mixture thickens and develops a golden caramel color, approximately 20 to 25 minutes.
05 - Increase heat and bring mixture to a rolling boil. Add liquid pectin and stir well. Continue to boil vigorously for 1 to 2 minutes, then remove from heat.
06 - Skim off any surface foam if necessary. Ladle hot mixture into sterilized jars, leaving a 1/4-inch headspace. Wipe jar rims, secure lids, and process jars in a boiling water bath for 10 minutes, adjusting for altitude if needed.
07 - Allow jars to cool completely before storing in a cool, dark place. Refrigerate after opening.