In a large saucepan, combine chopped apples, brown sugar, granulated sugar, apple juice, lemon juice, cinnamon, nutmeg, and salt. Stir well and bring to a gentle simmer over medium heat.
Reduce heat and let the mixture simmer for about 25-30 minutes, stirring occasionally, until the apples soften and the mixture thickens.
Use an immersion blender to slightly puree the mixture, leaving some apple chunks for texture. Stir in the caramel sauce and vanilla extract. Let simmer for another 5-10 minutes until glossy and thick.
Remove from heat and transfer to sterilized jars. Let cool before sealing and storing in the refrigerator. Use within 3 weeks, or process in a water bath canner for long-term storage.