In a medium skillet over medium heat, combine the peeled and finely diced Gala apples with dark brown sugar, ground cinnamon, salt, and lemon juice. Cook the mixture, stirring occasionally, for about 10 minutes until the apples are tender and deeply browned. Once done, remove from heat and chill the caramelized apples in the fridge until cool.

In a saucepan, melt the unsalted butter over medium heat, swirling it occasionally. Continue cooking until it turns golden brown and the milk solids sink to the bottom, creating a nutty aroma, which takes about 5–7 minutes. Remove from heat and let the brown butter cool in the fridge for 10 minutes.

In a large mixing bowl, whisk together all-purpose flour, baking soda, cream of tartar, ground cinnamon, salt, and cornstarch until evenly combined. Set this mixture aside.

In another bowl, whisk the cooled brown butter with dark brown sugar, granulated sugar, and vanilla bean paste until creamy. Next, add in the egg, mixing until smooth. Gently fold in the cooled caramelized apples.

Gradually fold the dry ingredients into the wet mixture using a spatula, being cautious not to overmix. Cover the bowl with plastic wrap and chill the dough in the fridge for 2 to 3 hours.

Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. Mix granulated sugar and ground cinnamon for the coating.

Using a cookie scoop, portion the chilled dough into balls and roll in the cinnamon-sugar mixture. Bake for 12 to 14 minutes, until the edges are lightly golden. Let them cool on the pan for 5 minutes before transferring to a wire rack.