01 - Place apples, granulated sugar, brown sugar, and apple cider or water into a large heavy-bottomed pot; stir until evenly mixed.
02 - Heat over medium, stirring occasionally, until apples break down and soften, approximately 20 to 30 minutes.
03 - Remove pot from heat; blend with an immersion blender or transfer in batches to a blender until completely smooth.
04 - Return puree to the pot; add cinnamon, cloves, allspice, nutmeg, salt, and lemon juice; stir thoroughly.
05 - Cook uncovered over low heat, stirring frequently to prevent sticking, until mixture thickens and develops deep brown color, about 1.5 hours; mixture should mound on a spoon without flowing off easily.
06 - Taste and modify spice levels or sweetness as preferred.
07 - Allow to cool slightly, then transfer to sterilized jars; refrigerate up to 3 weeks or process in a water bath for extended shelf life.