Preheat oven to 350F and line 2 baking sheets with parchment paper.

In a large mixing bowl, stir together coconut, sugar, egg white, and vanilla until combined.

Drop by teaspoonfuls onto prepared pans.

Bake for 7 minutes or until bottoms are lightly golden.

Allow cookies to cool on baking sheets.

Place 8 ounces of bittersweet chocolate in a mixing bowl and chop into small chunks.

In a small saucepan, heat whipping cream with butter until butter melts and bubbles form around the edge.

Pour hot cream over the chocolate and whisk until smooth.

Stir in rum.

Cover and refrigerate for about 1 hour or until firm.

Place 1 teaspoon of chocolate mixture on top of each cookie.

Smooth to form a dome shape.

Refrigerate for about 1 hour or until firm.

Line cooled baking sheets with waxed paper.

In the top of a double boiler over hot water, melt the remaining 4 ounces of chocolate with vegetable shortening.

Allow melted chocolate to cool for 3 minutes.

Set cookie on a fork and spoon the melted chocolate over the cookie until completely coated.

Place on waxed paper.

Refrigerate until chocolate sets, about 2 hours.