Preheat oven to 350°F (176°F) and prepare a 9x13-inch baking pan by lining with parchment paper, leaving an overhang for easy removal. Set pan aside.
Add softened butter, granulated sugar, and powdered sugar to the bowl of a stand mixer. Beat on medium speed until smooth and creamy. Mix in vanilla and salt until just combined. Gradually add all the flour and mix until a soft dough forms; be careful not to overmix.
Press just a little over half the dough into the bottom of the prepared pan. Refrigerate the rest, tightly covered, until it is time to use it. Bake for 25 minutes or until the edges are lightly golden. Remove from the oven.
While the base is baking, combine the unwrapped caramels and heavy cream in a medium pot over medium-low heat. Stir gently until melted and smooth, about 5–8 minutes, then pour over the cookie base. Use a spoon to spread the caramel evenly. Remove the reserved cookie dough from the fridge, crumble it into bits, and sprinkle it over the caramel.
Return the pan to the oven for an additional 25–30 minutes, or until lightly golden brown around the edges. Be careful not to overbake. Cool completely at room temperature, then cut into small squares. Store leftovers tightly wrapped in the fridge, as they are best enjoyed cold. If desired, sprinkle sea salt on top just before serving.
Notes
Storage: Store leftovers tightly wrapped in the fridge. These bars will keep for about a week and are best enjoyed chilled.