In a medium pan over medium heat, melt 2 tablespoons of unsalted butter. Add 2 diced Granny Smith apples along with 1/4 cup of light brown sugar. Stir occasionally for about 8-10 minutes, until the apples are tender and golden. Once done, transfer the caramelized apples to a paper towel to cool while you prepare the rest of the ingredients.

In a separate mixing bowl, whisk together 1 1/2 cups of all-purpose flour, 1 teaspoon of baking soda, 1 teaspoon of ground cinnamon, and a pinch of salt. Ensure there are no lumps in the flour mixture.

In a stand mixer, combine 1/2 cup of room temperature unsalted butter with 1/2 cup of granulated sugar and 1/4 cup of light brown sugar. Beat on medium speed until the mixture is light and fluffy, roughly 3-5 minutes. Add 2 large eggs one at a time, mixing thoroughly after each addition, followed by 1 teaspoon of vanilla extract.

Gradually add the flour mixture to the creamed butter, mixing on low speed until just combined. Then fold in 1 1/2 cups of rolled oats and gently incorporate the cooled caramelized apples.

Cover the cookie dough with plastic wrap and refrigerate for at least 1 hour. Preheat your oven to 350°F (175°C).

Line a baking sheet with parchment paper. Using a cookie scoop or tablespoon, drop mounds of dough onto the prepared baking sheet, spacing them about 2 inches apart. Bake in the preheated oven for 12-15 minutes.

Prepare the glaze by whisking together 1 cup of powdered sugar and 2-3 tablespoons of water until smooth. Drizzle the glaze over the cooled cookies.