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 about 10 minutes, stirring occasionally, until apples are tender.
02 - Lightly mash the cooked apples using a potato masher or immersion blender, leaving some small chunks for a rustic texture.
03 - Add granulated sugar, brown sugar, ground cinnamon, nutmeg, allspice, and salt. Stir until sugars are dissolved completely.
04 - Stir in cubed unsalted butter. Continue cooking over medium heat, stirring frequently and scraping the bottom to prevent scorching. Maintain heat until the mixture thickens and develops a deep golden caramel color, about 20 to 25 minutes.
05 - Increase heat, bring mixture to a rolling boil. Add liquid pectin and stir well. Boil hard for 1 to 2 minutes, then immediately remove from heat.
06 - Skim off any foam as necessary. Ladle the hot jam into sterilized jars, leaving 1/4-inch headspace. Wipe jar rims, apply lids, and process jars in a boiling water bath for 10 minutes, adjusting time for altitude as needed.
07 - Allow jars to cool completely on a towel-lined surface. Check seals, then store in a cool, dark place. Refrigerate after opening.