In a medium heavy-bottomed saucepan, combine the sugar, water, and corn syrup. Gently stir to moisten all the sugar, then stop stirring.

Set the pan over medium heat and cook undisturbed for 5–10 minutes, until the mixture turns deep amber. It takes at least 5 minutes for it to start turning brown, but keep an eye on it—once it starts changing color, it can go from amber to burnt quickly.

Meanwhile, warm the heavy cream in the microwave for about 1 minute.

Once the caramel reaches a rich copper color, remove it from heat and carefully pour in the warm cream slowly while whisking constantly—it will bubble up rapidly.

Whisk until smooth. Stir in the vanilla, salt, and butter. If needed, return to low heat briefly to fully smooth it out.

Let cool slightly, then transfer to a heat-safe jar and refrigerate until ready to assemble. The caramel will thicken as it cools.

Preheat oven to 350°F. Line two baking sheets with parchment paper.

Add the granulated sugar and brown sugar to the bowl with the melted butter. Whisk until the mixture is shiny and smooth—about 1 minute.

Add the chilled egg, egg yolk, and vanilla. Whisk vigorously until lightened in color and slightly thickened. It should almost double in volume.

Fold in the cornstarch, baking soda, cream of tartar, salt, cinnamon, and flour. Switch to a rubber spatula and fold the dough until no flour streaks remain.

In a small bowl, mix ⅓ cup granulated sugar with 1 teaspoon cinnamon for rolling.

Using a 2-tablespoon scoop, portion out dough and roll each ball in the cinnamon sugar. Place 12 dough balls per tray.

Bake for 8 minutes. Remove from the oven and gently flatten the tops with a flat spatula while still hot. Let cookies cool completely on a wire rack.

In the bowl of a stand mixer with the paddle attachment, beat the butter and cream cheese on medium speed for about 2 minutes until creamy and smooth.

Scrape down the sides and bottom of the bowl, then beat for another 2 minutes.

With the mixer on low speed, gradually add the powdered sugar. Once combined, add the cooled caramel sauce, vanilla extract, and a pinch of salt.

Make sure the caramel is fully cooled—if it's warm, it can cause the frosting to separate.

Increase mixer speed to medium and beat for 3–5 minutes until the frosting is smooth and fluffy.

Ensure the cookies are completely cooled before assembling.

Pipe a thick rim of cream cheese frosting around the edges of half of the cookies to create a well for the caramel. Be sure the rim is sturdy enough to hold the caramel but not overly thick.

Fill the frosting well with caramel sauce.

Top each frosted cookie with an unfrosted cookie and gently press them together to create sandwich cookies.