Set your oven to 350°F. Cover baking sheets with parchment paper and set aside.
In a medium microwave-safe bowl, combine caramel candies and heavy cream, microwave in 30-second intervals, stirring with a silicone spatula after each burst, until smooth. Set aside to cool.
In a stand mixer bowl fitted with the paddle attachment, beat softened butter, granulated sugar, and brown sugar on medium speed until smooth.
Add oil, egg, and vanilla extract. Mix well, using a rubber spatula to scrape down the bowl's sides frequently.
In a separate medium bowl, whisk together flour, cornstarch, baking powder, and salt. With the mixer on low speed, gradually add the dry ingredients to the butter mixture until the dough forms.
Fold in toffee pieces with a rubber spatula or wooden spoon until evenly distributed.
Using a large cookie scoop, portion dough onto prepared baking sheets, spacing cookies about 3 inches apart.
Press each portion with the bottom of a glass or flat measuring cup to flatten into a disc about ½ inch thick.
Bake for 10–12 minutes until edges just barely begin to brown and centers are set. Transfer baking sheets to a wire cooling rack and let cookies rest on sheets for 10 minutes, then move directly to rack to cool completely.
In another medium microwave-safe bowl, melt chocolate chips in 30-second bursts, stirring between intervals until smooth. Cool to room temperature.
Once cookies are completely cool, use a spoon or small offset spatula to spread caramel over each cookie's top.
Add a layer of melted chocolate over the caramel, spreading evenly with the back of a spoon or offset spatula.
Optional: Refrigerate or freeze assembled cookies for 10–15 minutes to set toppings faster