In the bowl of a stand mixer fitted with a paddle attachment, cream together softened butter, sugar, and powdered ube until smooth, about 3 minutes.
Add egg, ube extract, vanilla extract, and coconut milk. Mix on low speed until incorporated. Scrape down sides of bowl as needed to ensure thorough mixing.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Add dry mixture to mixing bowl. Mix on low speed until dough forms. Scrape down sides of bowl as needed. Be careful not to overmix.
Cover cookie dough. Chill in the refrigerator for at least one hour. Overnight is best.
Preheat oven to 350°F. Line baking sheets with parchment paper or silicone baking mat. Set aside.
Remove cookie dough from the fridge. If cookie dough has been chilled overnight, allow dough to sit at room temperature for 30-45 minutes before scooping.* Use a 1 ½ Tablespoon scoop (#40 scoop) to portion out the dough.
Roll cookie dough in your choice of sugar: granulated sugar, purple sanding sugar, or confectioners' sugar.
Place cookie balls 2-inches apart on prepared baking sheet. Bake for 13-15 minutes, until the edges of the cookies have set. Rotate baking sheet midway through baking. Rest in baking sheet for 3-5 minutes, then transfer cookies to wire rack to cool.