In a medium saucepan over medium heat, combine diced apples with brown sugar and cinnamon. Stir occasionally for about 5 minutes until the apples soften and become fragrant. Remove from heat and cool completely.

Cream together softened butter, dark brown sugar, and granulated sugar until fluffy, about 3-4 minutes. Add vanilla extract and the large egg, mixing until fully incorporated.

Whisk together all-purpose flour, baking soda, and salt in another bowl. Gradually add this to the wet ingredients, folding gently until combined.

Gently incorporate the cooled apple mixture into the cookie dough in two stages, ensuring even distribution without overworking the dough. Chill for 15 minutes if too soft.

Preheat your oven to 350 °F (175 °C) and line baking sheets with parchment paper. Scoop dough portions onto the trays, spaced 2 inches apart.

Bake for 10-12 minutes until edges are golden, but centers remain soft. Remove from oven and let cool slightly on a wire rack.

Drizzle the warm cookies with salted caramel sauce and let set before serving.