Prep: Set aside a nonstick or lined baking sheet for baking the cookies, plus an additional sheet or cutting board lined with a silicone mat or parchment paper for cutting the cookies. I also like to keep a bench scraper handy for easy cookie transfer, but a spatula will work as well.
Butter & Sugar: Add the butter and sugar to a stand mixer (or large bowl, using a handheld mixer). Cream together on low speed for 3 minutes, until the butter has lightened in color and looks fluffy.
Wet Ingredients: Add the ube extract and plant milk to the butter and cream over medium speed for about 1 minute, scraping the sides of the bowl as necessary, until the purple color is fully incorporated.
Dry Ingredients: Sift the flour and baking powder directly into the bowl using a fine metal or mesh sieve, stirring around with a spatula to combine the dry ingredients as they are sifted. Use the mixer to mix the dough until just combined, starting at a lower speed to prevent flour from spraying. The dough should look slightly crumbly, but will stick together and smooth out once pressed with a spatula.
Roll the dough: Dust the baking sheet lines with a silicone mat with flour, then transfer the dough to the baking sheet and sprinkle the top with flour. Use a floured rolling pin to roll out the dough until it is about ¼” thick. If the dough looks too sticky you can sprinkle it with additional flour.
Chill: Cover the dough with parchment paper or plastic wrap and place in the refrigerator to chill for 30 minutes.
Shape your Cookies: Use a cookie cutter to cut cookies out of the chilled dough and transfer them to a lined baking sheet. If you move quickly you may be able to re-roll the dough to get a second batch of cookies; if the dough is too sticky, return to the fridge for a few minutes before repeating.
Preheat: Return the cookie sheet to the fridge for one final chill (about 10-15 minutes) while you preheat the oven to 350F.
Bake: Bake the cookies in the middle rack of the oven for 9 minutes; they will look slightly puffy and soft. Remove from the oven and let the cookies cool on the baking sheet for at least 5 minutes before transferring to a cooling rack. Let cookies cool completely before decorating, if you plan to do so.