Preheat the oven to 375ºF (191ºC) and line a cookie sheet with parchment paper. Set aside.
Add the butter, brown sugar, and white sugar to the bowl of a stand mixer fitted with the paddle attachment, or a large bowl with an electric mixer.
Cream the butter and sugars together on medium speed until light and fluffy, approximately 2-3 minutes.
Add the egg and vanilla extract and mix on medium speed until lighter in color, or 1-2 minutes.
Pour in the rolled oats and coconut and mix just until combined.
In a separate large bowl, combine the flour, baking powder, salt, and baking soda. Whisk until well combined.
Add half of the flour mixture and mix on medium speed just until the flour is absorbed. Then add the other half and do the same. Be careful not to overmix - just enough so the flour is absorbed.
Use a cookie scoop or a heaping tablespoon to portion the dough into 1 ½” balls. Drop them on the prepared cookie sheet, spacing them 1 ½-2” apart (approximately 12 cookies per sheet).
Bake in the preheated oven for 10-12 minutes, or until the very edges are beginning to brown. The centers will look underdone, but that’s fine - they will be set up outside of the oven.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire cooling rack.
Repeat with the remaining cookie dough, alternating baking sheets if you have 2 or more.
Cool the cookies to room temperature, then serve or store them for later.