In a medium saucepan over medium heat, combine diced apples, brown sugar, and cinnamon. Stir gently for about 5 minutes until apples soften and sugar melts. Transfer to a bowl and let cool completely.

In a large mixing bowl, cream together softened butter, brown sugar, and granulated sugar until light and fluffy, about 2-3 minutes. Add vanilla extract and egg, beating until well combined.

In a separate bowl, whisk together all-purpose flour, baking soda, and salt. Gradually fold the dry ingredients into the wet mixture until just combined. Avoid over-mixing.

Gently fold the cooled apple mixture into the dough in two stages. If dough feels too soft, refrigerate for about 30 minutes.

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper. Use a cookie scoop to drop rounded tablespoons of dough onto sheets, leaving space between cookies. Bake for 10-12 minutes until edges are golden and centers are set but soft.

Once baked, let cookies sit on baking sheet for a few minutes before transferring to a wire rack to cool completely. Drizzle generously with salted caramel sauce.