In large bowl, whisk together flour, cornstarch, salt, baking powder, and baking soda until well combined; set aside.
In a separate large bowl, beat together brown sugar, granulated sugar, and 1 cup butter with an electric mixer on medium speed until well combined. Add egg, egg yolks, and 2 teaspoons vanilla, and beat until well combined.
Beat flour mixture into wet mixture until combined. Stir in coconut, pineapple, and rum extract.
Using a small ice cream scoop (about 2 teaspoons), ball up dough. Place on lined baking sheets (parchment, wax, or silpats), cover dough with plastic wrap, and refrigerate 2-3 hours, or overnight, or up to 2-3 days.
Preheat oven to 325 degrees F. Bake cookies in batches about 13-16 minutes or until slightly browned around edges.
Drizzle white chocolate over cookies with a fork. Cool completely so white chocolate sets.
SNAPPY TIPS: I strongly suggest refrigerating the dough for best results and not baking right away. I put the pineapple and coconut in a food processor to quickly chop, although the coconut does not need to be chopped.SNAPPY SUBSTITUTIONS: I do not suggest substituting margarine for butter, whole eggs for the egg yolks. Results will vary a lot the more you substitute.