In a medium-sized saucepan, combine water, granulated sugar, and corn syrup. Use at least a 2-quart pan to prevent overflow.
Over medium heat, bring the sugar mixture to a boil. Do not stir during this process to avoid crystallization.
Let the mixture boil until it turns golden brown, around 5-7 minutes. Watch carefully to avoid burning.
Warm the cream in the microwave for 1 minute.
Once the caramel achieves a golden brown color, remove from heat and carefully add the warm cream. Stir until combined.
Transfer the caramel mixture to a separate bowl, then add vanilla, salt, and butter. Let it sit until the butter melts, and then stir until well incorporated.
For the Cookies
Preheat the oven to 350 degrees F. Line 3 sheet pans with parchment paper. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter, oil, granulated sugar, and powdered sugar on medium speed.
Add the eggs, one at a time, mixing after each addition. Cream on medium speed for 30 seconds after each egg is added. Scrape down the bottom and sides of the bowl.
Add in the vanilla, sour cream, and coconut extract. Mix just until combined.
Add the baking soda, baking powder, salt, and flour. Mix on the lowest speed until no flour streaks remain and the mixture is evenly combined; don’t overmix.
Scoop the dough into about 3-tablespoon sized portions and roll into balls. Place several inches apart on the prepared baking sheets.
Using a flat surface, like a pancake spatula, or the bottom of a cup with a flat surface, press down each ball slightly. Aim for a thickness of about ½ inch.
Bake the cookies for 10-12 minutes until just set. Avoid browning.
Let the cookies cool for a few minutes on the baking sheets before transferring to a cooling rack to cool completely.
For the Cream Cheese Frosting
In the bowl of an electric mixer, combine the butter, cream cheese, caramel sauce, and cream on medium speed for about two minutes. Scrape down the sides and bottom of the bowl. Beat again for 2 more minutes.
With the mixer on low speed, add the powdered sugar and salt. Beat on low just until mixed. Then turn the mixer to medium-high speed and beat the mixture for 2-3 minutes.
Add the vanilla and coconut extract and mix on low just until combined.
Assembly
Once the cookies are completely cooled, frost them with a small offset spatula and spread the frosting evenly to the edge of the cookie.
OPTIONAL: Coat half of the cookies with toasted shredded coconut and half with caramel.
Use the tip of the offset spatula to swirl some salted caramel on top of the cream cheese frosting.
Note: These cookies are best enjoyed chilled from the fridge.