Make the apple mixture. Add the chopped apples, brown sugar and cinnamon to a small frying pan. Cook over medium heat while stirring frequently and for about 5 minutes until the apples soften just slightly but still stay intact (do not cook them down until they’re mushy). Transfer to a clean bowl and let cool completely.
Make the cookie dough. Combine soft butter, both sugars and vanilla extract in a large bowl and beat using an electric hand mixer or a stand mixer for 1-2 minutes on medium speed until it is pale and fluffy. Beat in the egg until well combined.
Combine flour, baking soda and salt in a medium bowl and whisk to blend evenly. Add the dry ingredients to the butter mixture and fold it in gently until mostly incorporated.
Add the apple mixture. We are going to mix the apple mixture into the dough in two stages to minimize the amount of mixing that is required to incorporate it evenly. Add half of the apples to the dough and fold it in. It's ok if you use a little force. Add the remaining apples and fold it into the cookie dough. Do not add any of the liquid that comes out of the apples. If your dough is very soft, you can refrigerate it for 20 minutes.
Preheat your oven to 350°F. Line 2 large baking sheets with parchment paper.
Use a medium spring-loaded ice cream scoop or two large spoons to scoop mounds of dough onto baking sheets. This makes 12-15 cookies. Bake for 12-16 minutes until browned around the edges and on the bottoms, and lightly golden on top. If you make 12 larger cookies, then it will take closer to 16 minutes. Let them cool for 2 minutes on the baking sheets and then transfer to a wire rack to finish cooling. Drizzle with salted caramel sauce and enjoy!