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:
Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper. Set aside.
In a stand mixer fitted with the paddle attachment, cream the cold, cubed butter and brown sugar on medium-high speed until light and fluffy (about 2-3 minutes). Add the pumpkin puree and mix until combined.
Add the egg and vanilla, and beat until smooth (about 30 seconds).
Add the flour, baking powder, pumpkin pie spice, cinnamon, and salt, and mix on low speed just until combined. Avoid overmixing.
Use a large cookie scoop (about 3 tablespoons) to portion out 12-14 cookie dough balls and place them on the prepared baking sheet.
Lightly spray the tops of the cookie dough balls and flatten slightly to about ½ inch thickness.
Bake for 15-16 minutes. Allow the cookies to cool on the baking sheet before transferring them to a cooling rack.
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:
Once the cookies are completely cooled, spread or pipe the cream cheese frosting onto the cookies.
Use the tip of an offset spatula to swirl a bit of salted caramel on top of the cream cheese frosting.
Serve at room temperature or chilled. These cookies can be stored at room temperature for up to 3-4 days or refrigerated in an airtight container for up to 7 days.
Note: These cookies are best enjoyed chilled from the fridge!