Combine the chopped apples and water in a large, heavy-bottomed Dutch oven or stockpot. Cover and cook over medium heat for 15-20 minutes, stirring occasionally, until the apples have broken down significantly and are very soft.

Remove the pot from the heat. Using an immersion blender, or carefully transferring in batches to a standard blender, blend the apple mixture until completely smooth. If using a traditional blender, ensure the lid is vented and covered with a towel to allow steam to escape.

Return the smooth puree to the pot. Stir in the brown sugar, cinnamon, allspice, cloves, and salt until fully incorporated.

Bring the mixture to a simmer over medium-low heat. Reduce the heat to the lowest possible setting that still maintains a gentle bubble. Cook uncovered for 3 to 4 hours, stirring every 20-30 minutes, especially towards the end, to prevent sticking and scorching on the bottom.

The apple butter is done when it has darkened significantly, thickened to a spreadable, rich consistency, and coats the back of a spoon thickly. It should hold a shape when spooned onto a plate.

Remove from heat and let cool slightly before transferring to sterilized jars. Store in the refrigerator for up to 3 weeks, or process using standard canning methods for long-term shelf stability.