Start by peeling and finely dicing your gala apples. In a medium bowl, toss the apples with dark brown sugar, ground cinnamon, a pinch of salt, and a squeeze of lemon juice. Heat a skillet over low to medium heat and cook the apples for about 10 minutes until they become beautifully browned and caramelized. Set them aside to chill in the fridge.
In a pot over medium heat, melt the unsalted butter. Stir occasionally until it turns a lovely golden brown color. Remove it from heat and transfer it to another container to cool in the fridge for about 10 minutes.
Whisk together all the dry ingredients in a separate bowl: all-purpose flour, baking soda, cream of tartar, ground cinnamon, fine sea salt, and cornstarch.
In another bowl, whisk together your cooled brown butter with both dark brown sugar and granulated sugar until smooth. Add in your vanilla bean paste or extract, then mix in one egg and an additional egg yolk until combined. Gently fold in the chilled caramelized apples.
Gradually add your dry ingredients to the wet mixture. Gently fold them together until just combined. Cover tightly and let it chill in the fridge for about 2-3 hours.
Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper. In a small bowl, mix together granulated sugar and ground cinnamon for coating your cookies.
Using a cookie scoop, roll your chilled dough into balls and coat in the cinnamon-sugar mixture. Place them on the baking sheet with space between each ball. Bake for about 12-14 minutes until edges are set and golden brown.