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, gently mash the softened apples, leaving some small pieces for texture.
03 - Stir in granulated sugar, brown sugar, cinnamon, nutmeg, allspice, and salt. Mix thoroughly until sugars dissolve.
04 - Add the butter. Continue cooking over medium heat, stirring frequently and scraping the bottom of the pot, until mixture thickens and turns a golden caramel shade, about 20 to 25 minutes.
05 - Increase heat to bring the mixture to a rolling boil. Add the liquid pectin, stir well, and continue boiling firmly for 1 to 2 minutes. Remove pot from heat.
06 - Skim off any foam if present. Ladle the hot jam into pre-sterilized jars, leaving 1/4-inch headspace. Wipe jar rims, secure lids, and process in a boiling water bath for 10 minutes, adjusting for altitude if necessary.
07 - Allow processed jars to cool completely at room temperature. Verify seals and store in a cool, dark place. Once opened, refrigerate.