In a medium saucepan, stir together the water, sugar, and corn syrup.
Heat over medium until it begins to boil. Once boiling, do not stir to avoid crystallization.
Continue boiling until the mixture turns golden brown. Be cautious as it can burn quickly.
Meanwhile, microwave the heavy cream for 1 minute to warm it.
Once the caramel reaches a golden color, remove from heat and slowly add the warm cream while whisking constantly.
Stir in the vanilla extract, salt, and butter until fully combined.
Transfer the caramel to a bowl and let it cool.
For the cookies
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and both sugars together on medium speed until light and fluffy, about 2 minutes. Scrape down the sides of the bowl with a rubber spatula halfway through.
Add the egg and mix on medium speed until fully incorporated, about 30 seconds. Then mix in the vanilla extract, molasses, and water on low speed until evenly combined.
In a separate bowl, whisk together the flour, ground ginger, baking soda, cinnamon, cloves, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just incorporated. Ensure there are no flour streaks, but do not overmix.
Scoop the dough into balls using a 3-tablespoon cookie scoop. Arrange the balls on a lined baking sheet or plate, ensuring they don’t touch, and refrigerate for 15-20 minutes.
While the dough chills, preheat your oven to 350°F and line two cookie sheets with parchment paper.
Once chilled, place 9 dough balls on each prepared cookie sheet, spacing them 2-3 inches apart to allow for spreading.
Bake the cookies for 11 minutes, or until the edges are set. Once they are hot and out of the oven, use a flat surface and gently press each one so they are flat! Let them cool completely on the baking sheets before assembling.
For the Cream Cheese Frosting:
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.
Increase mixer speed to medium and beat for 3-5 minutes until the frosting is smooth and fluffy.
Assembly
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. I added melted white chocolate on top for fun, but not necessary!