In a medium bowl, whisk together all of the dry ingredients: all-purpose flour, baking soda, and salt.
In a stand mixer using the paddle attachment, cream the melted butter and both sugars on medium speed until smooth and fluffy, about 2 minutes.
Add egg, rehydrated ube, and ube extract to the bowl. Mix until combined, about 10-20 seconds.
Add all of the dry ingredients to the stand mixer and pulse a few times until it is mostly incorporated. Add all of the white chocolate and shredded coconut. Pulse a few more times.
Use cookie scoop to form dough into balls (about 1.5-2 tablespoons each) and place them on a lined baking sheet or plate. Refrigerate dough for at least 30 minutes.Note: If you want to bake these later, you can put the sheet/plate in the freezer. Once the dough balls are frozen, you can transfer them to an airtight container or bag for up to 3 months. You can bake them right from the freezer, but you may have to increase the baking time by 2-3 minutes.
Place oven rack in the middle of the oven. Preheat the oven to 350°F/177°C.
Line two baking sheets with parchment paper/silicone mats and place dough balls on top, at least 3 inches apart. Bake for 10-13 minutes, until edges are slightly browned. Immediately sprinkle flaky sea salt on top. Optional: Once the cookies come out of the oven, you can gently push in a few white chocolate chips on the top of each cookie for the ~aesthetic~. If you want the cookies to be circular, take a large circular biscuit cutter or something wider than your cookies, like the rim of a mug. Place the circular cutter on top of your still warm cookie while it is still on the baking sheet. Move the cookie around in the cutter in a circular motion. This pushes the sides of the cookie towards the center, forcing it to mold into a circular shape. (more details can be found here: https://food52.com/blog/23550-best-chocolate-chip-cookies-how-to-make-round) Allow to cool on sheet for at least 5 minutes.