In a medium saucepan over medium heat, combine diced apples, brown sugar, and cinnamon. Cook for about 5 minutes, stirring frequently, until softened and fragrant.

In a mixing bowl, cream together the unsalted butter, dark brown sugar, and granulated sugar until light and fluffy, about 2-3 minutes. Add the egg and a splash of vanilla extract, mixing until well incorporated.

In a separate bowl, whisk together all-purpose flour, baking soda, and salt. Gradually incorporate this dry mixture into the wet mixture, folding gently until just combined.

Gently incorporate the cooled apple mixture into the dough, folding in stages. If too soft, refrigerate for 15-30 minutes.

Preheat oven to 350°F (175°C) and line baking sheets with parchment paper. Drop dough onto sheets, spacing about 2 inches apart. Bake for 10-12 minutes until golden brown around the edges.

Let the cookies cool for about 5 minutes before transferring to a wire rack. Drizzle cooled cookies with salted caramel sauce.