Preheat the oven to 325°F. Line a baking sheet with parchment paper and set it aside.
Using a handheld mixer, combine the butter, shortening, sugar, eggs, and vanilla in a large bowl.
To the butter mixture, add the flour, cornstarch, salt, and baking powder. Mix until the ingredients are incorporated.
Using a ¼ cup (or 2 scoops of dough with a 2 tablespoon scoop), add the dough out onto a lined cookie sheet, about 2 inches apart. (I usually put 6 cookie dough balls onto each cookie sheet.)
Use the bottom of a glass to slightly flatten each ball of dough to ¼ to ½-inch thickness. (If you used two 2-tablespoon scoops, combine the scoops of dough into one large cookie.)
Bake for 12 minutes for a softer cookie, up to 14 minutes for a firmer cookie.
Remove cookies from the oven and let them cool on a wire rack while you prepare the caramel.