Step 1: Puree the peaches in a blender or food processor until completely smooth. You can leave the skins on for a deeper color or peel them if preferred.
Step 2: Transfer the peach puree to a large slow cooker (6-quart capacity recommended).
Step 3: Stir in the granulated sugar, brown sugar, lemon juice, cinnamon, cloves, and salt until well combined.
Step 4: Cover the slow cooker but prop the lid open slightly with a wooden spoon or a heat-resistant spatula to allow steam to escape.
Step 5: Cook on LOW for 8-10 hours or until the mixture has thickened and reduced by nearly half, turning a deep amber color.
Step 6: Stir in the vanilla extract during the last 30 minutes of cooking. Use an immersion blender for an extra-smooth finish if desired.
Step 7: Ladle the hot peach butter into clean jars. Allow to cool completely before refrigerating or follow standard water-bath canning procedures for long-term storage.