Begin by dicing medium tart apples and adding them to a skillet over medium heat. Combine the apples with unsalted butter, light brown sugar, ground cinnamon, and a pinch of salt. Stir occasionally for about 5-7 minutes until the apples soften and become fragrant. Mix in cornstarch and a splash of water to thicken, cooking for an additional 2-3 minutes. Allow the apple filling to cool before use.

In a large mixing bowl, whisk together all-purpose flour, baking powder, baking soda, granulated sugar, and ground cinnamon. Combine thoroughly and set aside.

In another bowl, beat together the unsalted butter and remaining granulated sugar until fluffy, about 3-5 minutes. Add the egg, egg yolk, and vanilla extract, mixing until incorporated. Gradually fold in the dry ingredient mixture until combined.

Cover the dough with plastic wrap and chill in the refrigerator for 20-30 minutes. While chilling, preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.

Scoop tablespoon-sized balls of dough onto prepared baking sheets, spacing them about 2 inches apart. Create a well in the center of each dough ball and fill with cooled apple filling carefully.

Bake the cookies for 10-12 minutes until edges are golden brown while centers remain soft. Allow to cool on baking sheets for 5 minutes before transferring to wire racks.

Prepare the caramel drizzle by melting soft caramel candies with heavy cream in a microwave-safe bowl, heating in increments until smooth. Drizzle over cooled cookies and sprinkle with flaky sea salt.

Allow the caramel drizzle to set for about 15-20 minutes at room temperature before serving.