01 - Combine chopped apples, lemon juice, apple cider, and water in a large heavy-bottomed pot. Bring to a simmer over medium heat, stirring occasionally. Cook for 10 minutes, or until apples are tender.
02 - Lightly mash apples using a potato masher or immersion blender, leaving some small chunks for texture.
03 - Add granulated sugar, brown sugar, cinnamon, nutmeg, allspice, and salt. Stir until sugars are fully dissolved.
04 - Stir in butter. Continue to cook on medium heat, stirring frequently, until mixture thickens and develops a golden caramel hue, about 20 to 25 minutes. Scrape the bottom regularly to prevent burning.
05 - Bring mixture to a boil. Add liquid pectin, stir thoroughly, and boil hard for 1 to 2 minutes. Remove pot from heat.
06 - Skim off any foam if present. Ladle hot mixture 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 necessary.
07 - Allow jars to cool completely. Store sealed jars in a cool, dark location. After opening, refrigerate and consume promptly.