In a large mixing bowl, whisk together butter and sugar until smooth using an electric mixer or by hand using a whisk. Mix in flour, baking powder and salt, followed by the vanilla and milk, adding in the milk as needed to make the dough come together without being sticky. (Add in a bit of extra flour if your dough is very sticky.)
Roll the dough out between two pieces of parchment paper to about ¼-inch thickness and use a 1½-inch cookie cutter (or a small inverted drinking glass) to cut the dough into rounds. Place on a parchment-lined baking sheet. Bake cookies for 10-12 minutes, until bottoms are lightly browned and cookies are set. Cool completely.
Preheat oven broiler on low. Spread the coconut evenly on a parchment-lined baking sheet and toast, stirring every 1-2 minutes, until coconut is golden brown. Cool on baking sheet, stirring occasionally. Then mix with the caramel.
Using a microwave melt the chocolate in a bowl in 20-second increments, stirring after each time until the chocolate is melted and smooth. Dip the top of each cookie into the chocolate and place on a clean piece of parchment paper.
Spread the coconut caramel mixture on top of each cookie. Lightly drizzle the tops with some of the remaining melted chocolate.
Let chocolate set completely before serving (can be placed in the refrigerator to speed up cooling).
Make a day in advance if desired. Store cookies in an airtight container.
Notes
Working with the caramel and coconut mixture can get difficult if it begins to harden before you have coated all the cookies. If this happens, simply move the pan back to the stove on low heat for 2-3 minutes to allow the mixture to warm again.