Begin by peeling and finely dicing the Gala apples. In a medium skillet, combine the diced apples with dark brown sugar, ground cinnamon, a pinch of salt, and a splash of lemon juice. Cook over low-medium heat for about 10 minutes until the apples are tender and caramelized, stirring occasionally. Once done, transfer the mixture to the fridge to cool completely.

In a saucepan, melt the unsalted butter over medium heat, stirring constantly. Watch for the butter to turn golden brown, approximately 5-7 minutes, as the milk solids begin to float and turn slightly darker. Remove the saucepan from the heat and let the brown butter cool in the fridge for about 10 minutes.

In a large mixing bowl, whisk together the all-purpose flour, baking soda, cream of tartar, ground cinnamon, fine sea salt, and cornstarch until well combined. Set the bowl aside.

In a separate bowl, whisk together the cooled brown butter, dark brown sugar, granulated sugar, and vanilla bean paste until smooth. Add the room temperature egg and egg yolk, mixing until fully incorporated. Gently fold in the cooled caramelized apples.

Gradually add the dry ingredients into the wet mixture, stirring gently until just combined. Cover the bowl with plastic wrap and chill in the refrigerator for 2-3 hours.

While the cookie dough chills, preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.

Once the dough is chilled, use a cookie scoop or spoon to portion out the dough into equal-sized balls. Roll each ball in a mixture of granulated sugar and ground cinnamon to coat thoroughly. Place the dough balls on the prepared baking sheet, spacing them 2-3 inches apart.

Bake the cookies in the preheated oven for 12-14 minutes, or until their edges are golden and the tops are puffy. Allow the cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.