In a large mixing bowl, cream together softened unsalted butter, granulated white sugar, and packed brown sugar until light and fluffy, about 3-4 minutes. Use an electric mixer for best results.

Add egg and egg yolk (both at room temperature) one at a time, mixing well after each addition. Then, mix in pure vanilla extract.

In a separate bowl, whisk together all-purpose flour, baking powder, ground cinnamon, allspice, and sea salt.

Gradually add the dry ingredients to the wet mixture, mixing until a soft dough forms.

Refrigerate the dough for 30 minutes to firm it up and make it easier to roll into balls.

Preheat the oven to 350°F.

In a small bowl, combine ½ cup granulated white sugar and ½ teaspoon ground cinnamon for rolling the cookie dough balls.

Take the dough out of the refrigerator, scoop about 1 tablespoon of dough, and form it into a ball.

Roll the dough ball in the cinnamon-sugar mixture until fully coated.

Place the coated dough balls on a parchment-lined baking sheet, spaced about 2 inches apart.

Bake the cookies for 9-10 minutes. The edges should be lightly golden, while the centers will be puffed and slightly underbaked.

Remove from the oven and let the cookies rest on the baking sheet for 1 minute. Use the back of a tablespoon or press the bottom of a small glass to create an indentation in the centers for the apple filling.

Dice the apples into bite-sized chunks.

Melt unsalted butter in a medium-sized skillet over medium heat. Add the diced apples, brown sugar, ground cinnamon, and a pinch of salt. Heat until it starts to bubble.

Cook and stir for about 5-7 minutes, until the apples soften and the mixture is caramelized.

Add lemon juice, stir, and remove the skillet from the heat.

Transfer the apple mixture to a medium bowl to cool, either at room temperature or in the refrigerator.

In a heavy-bottomed saucepan, heat superfine granulated sugar over medium heat. Stir continuously until the sugar melts and turns into a golden-caramel syrup.

Carefully add unsalted butter to the melted sugar and reduce the heat slightly. Stir until the butter is fully incorporated.

Remove the pan from the heat and gradually pour in the heavy cream while stirring constantly. Be careful, as the mixture will bubble up vigorously.

Return the pot to the heat for an additional 2 minutes, until the caramel thickens.

Remove from the heat, then stir in a pinch of flaky sea salt and pure vanilla extract. Let the caramel sauce cool slightly, about 10-15 minutes before using.

Spoon a small amount of the cooled apple filling into the indentation of each cooled cookie.

Drizzle the salted caramel sauce over the apple-filled cookies.