Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
Mix dry ingredients: In a bowl, whisk together flour, cornstarch, baking powder, and salt. Set aside.
Cream butter and sugar: In a large bowl, beat butter and sugar for 2–3 minutes until light and fluffy.
Add wet ingredients: Mix in the egg, egg yolk, vanilla extract, coconut extract, pineapple extract, rum extract (if using), and coconut milk until smooth.
Add pineapple powder: Mix in the finely ground freeze-dried pineapple powder until evenly incorporated.
Combine: Gradually add dry ingredients and mix just until combined. Do not overmix.
Chill dough: Cover and chill for 30–45 minutes.
Shape cookies: Scoop 2-tablespoon portions, roll into smooth balls, then roll in the sugar and salt mixture.
Bake: Place on prepared baking sheets and bake for 10–11 minutes, until edges are set and centers remain soft.
Cool: Let cookies rest on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.