Preheat the oven to 350°F and line two baking sheets with parchment paper.
Cream the softened butter and the sugar in the bowl of a stand mixer fitted with the paddle attachment until smooth and fluffy, then mix in the vanilla extract and the milk until combined.
Add the flour, the baking powder, and the salt, mixing on low speed until a soft dough forms and no dry flour remains.
Roll the dough on a lightly floured surface to about ¼-inch thick and cut out 2½-inch circles, then remove the centers with a 1-inch cutter to form donut shapes, rerolling scraps as needed.
Transfer the cookies to the prepared baking sheets and freeze them for about 10 minutes to help them hold their shape.
Bake the cookies for about 10 minutes until just set without browning, then cool them completely.
Spread the coconut flakes on a rimmed baking sheet and toast them at 350°F for about 10 minutes, stirring every few minutes, until golden and fragrant, then cool completely.
Heat the unwrapped caramels and the evaporated milk in a wide skillet or heavy saucepan over low heat, stirring constantly with a silicone spatula until melted and smooth, about 10 minutes.
Spread a thin layer of the caramel over each cooled cookie with an offset spatula or butter knife.
Stir the toasted coconut into the remaining caramel and let the mixture cool slightly until easier to handle.
Place about 1 tablespoon of the coconut-caramel mixture onto each cookie and gently shape it to fit, working quickly as the caramel firms.
Melt the chocolate wafers and the vegetable oil in the microwave in 30-second intervals, stirring until smooth.
Dip the bottoms of the cookies into the melted chocolate and place them on parchment paper to set. Let some of the chocolate drip off before setting them down.
Drizzle the remaining chocolate over the tops using a piping bag or zip-top bag with the corner snipped, then let the chocolate fully set before serving or storing.