01 - Combine chopped apples, lemon juice, apple cider, and water in a large heavy-bottomed pot. Set over medium heat and bring to a simmer. Cook, stirring occasionally, until apples are tender, about 10 minutes.
02 - Using a potato masher or immersion blender, mash apples lightly, keeping some small chunks for texture.
03 - Stir in granulated sugar, brown sugar, cinnamon, nutmeg, allspice, and salt. Mix well until sugars are fully dissolved.
04 - Add cubed unsalted butter. Continue cooking over medium heat, stirring frequently and scraping bottom, until mixture thickens and begins to caramelize with a golden hue, about 20 to 25 minutes.
05 - Increase heat and bring mixture to a boil. Stir in liquid pectin, boiling vigorously for 1 to 2 minutes while stirring constantly. Remove from heat.
06 - Skim off any surface foam. Ladle hot jam into sterilized jars, leaving 1/4-inch headspace. Wipe rims clean, affix lids, and process jars in a boiling water bath for 10 minutes, adjusting time if necessary for altitude.
07 - Let processed jars cool fully. Store in a cool, dark place. Refrigerate after opening.