Prepare Caramel: In a medium saucepan, combine salted butter and dark brown sugar over medium heat. Stir constantly until melted and bubbly, about 3 minutes. Add apple cider and boil gently for 10 minutes, stirring occasionally. Remove from heat and let cool slightly before chopping into small caramel pieces.

Dry Apples (optional): Preheat your oven to 350°F. Slice apples thinly and arrange them on a baking sheet lined with parchment paper. Bake for 10 minutes to reduce moisture and enhance their flavor. Let them cool.

Brown Butter: In a small saucepan, melt salted butter over medium heat until it turns golden brown, with a nutty aroma, about 5-7 minutes.

Mix Wet Ingredients: In a large mixing bowl, combine browned butter, dark brown sugar, room-temperature eggs, and vanilla extract. Beat until smooth and creamy, about 2 minutes.

Combine Dry Ingredients: In a separate bowl, whisk together all-purpose flour, old-fashioned oats, baking soda, and salt. Gradually add to the wet ingredients, mixing until just combined. Fold in chopped caramel and any dried apples.

Shape Cookies: Scoop dough using a rounded tablespoon and form into balls. Place on a lined baking sheet, leaving 2 inches between each. Chill the dough for at least 30 minutes.

Bake: Preheat oven to 350°F if not done. Bake cookies for 8 minutes, rotate baking sheet, and bake an additional 3-4 minutes until edges are set.

Cool & Glaze: Let cookies cool on baking sheet for about 5 minutes before transferring to a wire rack. Make the glaze by whisking together powdered sugar, maple syrup, a splash of vanilla, and a pinch of salt. Drizzle over cooled cookies.