In a large bowl, beat together ½ cup of the shortening and sugar until light and fluffy, then add in the vanilla. In a separate bowl, whisk together the flour, cornstarch and 1 teaspoon salt. Add to the shortening mixture; mix until combined. Form the dough into a ball; divide into 2 disks. Wrap each in plastic wrap; refrigerate for 45 minutes.
Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper. Roll out the dough to a 1/8-inch thickness and cut out, using a 1½-inch cookie cutter. Place cookies about 1 inch apart on the prepared baking sheet; bake until golden around the edges, 10 to 12 minutes. Let cool in the pan for 5 minutes; transfer to a wire rack to cool completely.
In a 2-quart saucepan over low heat, melt the caramels with the milk, stirring frequently. When smooth, reserve ¼ cup of the caramel. Add the remaining ½ teaspoon salt and the toasted coconut; stir to coat. Remove from the heat.
Line a baking sheet with parchment paper. Using an offset spatula, spread the tops and sides of the cookies with the reserved caramel and set on the prepared baking sheet. Let cookies stand for 45 minutes.
Using a double boiler or a metal bowl set over a pot of simmering water, melt together the chocolate chips and remaining 2 tablespoons shortening until smooth. Remove from the heat.
Dip the bottom of each cookie in the chocolate coating and return to the baking sheet. Then, using a spoon, drizzle the remaining chocolate in stripes on the cookie tops.