01 - Combine chopped apples, lemon juice, apple cider, and water in a large heavy-bottomed pot. Bring to a simmer over medium heat and cook for 10 minutes, stirring occasionally, until apples are tender.
02 - Use a potato masher or immersion blender to gently mash the softened apples, keeping some small chunks for added texture.
03 - Add granulated sugar, brown sugar, cinnamon, nutmeg, allspice, and salt. Stir until sugars dissolve completely.
04 - Stir in the cubed butter. Continue to cook on medium heat, stirring frequently, until the mixture thickens and develops a golden caramel color, around 20 to 25 minutes. Scrape the bottom regularly to avoid scorching.
05 - Bring the mixture to a rolling boil. Stir in the liquid pectin and boil vigorously for 1 to 2 minutes. Remove pot from heat.
06 - Skim off any foam if present. Carefully ladle hot jam into sterilized half-pint jars, leaving 1/4-inch headspace. Wipe jar rims, apply lids, and process jars in a boiling water bath for 10 minutes, adjusting for altitude if necessary.
07 - Allow jars to cool completely on a towel-lined counter. Once cooled, store sealed jars in a cool, dark area. Refrigerate after opening.