Preheat the oven to 350 degrees Line a large sheet pan with parchment paper and set aside.
In a large bowl, cream the 2/3 cup white sugar, powdered sugar, and room temperature butter until fluffy and light. Add the vegetable oil, vanilla extract, the egg, and heavy cream and mix until smooth.
In a smaller bowl, whisk together the flour, baking soda, cream of tartar, and salt. Combine wet and dry and mix until just combined.
Roll dough into balls the size of golf balls and place 2 inches apart on the prepared baking sheet.
Add the remaining 3 tablespoons sugar to a small bowl. Dip the bottom of a glass into the sugar and then press the dough balls with the jar dipped in sugar until the cookies are about 1/2 centimeter thick in the center and the edges crack (like the pictures).
Bake for 7-8 minutes. (The cookies look slightly undercooked, but are done!)
Let the cookies sit on the baking sheet for a few minutes before transferring them to a cooling rack.
Cream Cheese Frosting
Meanwhile, prepare the frosting. Using a hand mixer, cream together the room temperature butter and cream cheese on medium-high speed until completely smooth. Mix in vanilla extract, sea salt and cinnamon. With mixer running on low speed, slowly add powdered sugar and beat until well blended and smooth. Chill the frosting while the cookies finish cooling.
Frost completely cooled cookies with cream cheese frosting.
Caramel Drizzle
Unwrap the caramels and add them along with the heavy cream to a small saucepan over medium low heat. Stir until completely smooth and then set aside to slightly cool and thicken.
Once thickened and cooled, drizzle over cookies and add a sprinkle of sea salt.
Only add caramel and sea salt to the cookies that will be eaten immediately. Enjoy!