In a large bowl, beat the softened butter with an electric mixer on medium-high speed until creamy. Add the granulated sugar and brown sugar, and beat together for about 1 minute until light and fluffy. Mix in the vanilla and eggs until just combined. Add the flour, baking soda, baking powder, salt, cinnamon, nutmeg, allspice, and cloves, and stir until a cohesive dough forms. Cover and refrigerate for 30 minutes to make rolling easier.

Peel and core the apples, then dice them into small, even pieces. In a medium saucepan over medium-high heat, combine the diced apples, cubed butter, apple cider, brown sugar, cinnamon, nutmeg, and cloves. Cook, stirring occasionally, for 15 to 18 minutes, until the apples are tender and the mixture has thickened slightly. Transfer to a bowl and let cool completely at room temperature or in the fridge.

In a heavy-bottomed saucepan over medium heat, melt the granulated sugar, stirring constantly, until it turns a deep amber color. Remove from heat and immediately whisk in the cubed butter until melted. Slowly pour in the heavy cream while whisking (the mixture will bubble vigorously). Stir in the flaky sea salt. Let the caramel cool at room temperature for about 20 minutes until it thickens to a drizzle-able consistency.

Using a large cookie scoop (about 2.3 ounces or 65 grams per ball), portion the dough into balls. Place the dough balls in an airtight container and refrigerate for at least 4 hours, or freeze for 2 hours, before baking. Chilling the dough balls solid is essential for the best texture.

Preheat the oven to 350°F. In a medium bowl, stir together the melted butter, brown sugar, granulated sugar, flour, cinnamon, and salt until a crumbly mixture forms. Spread the crumble onto a parchment-lined baking sheet and bake for 12 to 14 minutes, until deep golden brown. Let cool on the pan, then break into smaller pieces as desired.

Preheat the oven to 365°F. Line baking sheets with parchment paper or silicone mats. In a small bowl, whisk together the sugar and spices for the coating. Roll each chilled dough ball in the cinnamon sugar mixture until coated. Place 6 cookies per sheet, spacing them about 3 inches apart. Bake for 10 to 12 minutes, until the edges are set and the centers look slightly underdone. Let rest on the baking sheet for 1 to 2 minutes, then use the back of a tablespoon to gently press an indent into the center of each cookie. Transfer to a wire rack to cool completely.

Spoon a generous amount of the cooled apple filling into the indentation of each cookie. Sprinkle the crumble over the filling, then drizzle with the salted caramel sauce. Serve immediately.