Preheat the oven to 350°F.
Place 1 cup of sweetened shredded coconut and 1 cup of unsweetened shredded coconut on a plate or in a shallow bowl and set it aside.
In the bowl of a food processor, place the rest remaining 2 cups of shredded coconut, sugar, salt, and baking powder. Process this into a coarse meal.
Add the butter and process again until the butter is incorporated and there are no lumps.
Add the egg and vanilla extract and process again until smooth.
Add the flour to the processor and pulse until the flour is incorporated and a dough starts to form. Scrape down the sides of the bowl as needed. The dough can be a little more like crumbs. No need to overmix it.
Making 6 at a time, take 1 tablespoon of dough and roll it into a ball. Repeat and place the 6 balls in the coconut on the plate or in the shallow bowl. Gently press each ball just a bit so the coconut will stick on all sides of each cookie. Place the cookies on a parchment-lined baking sheet about 1-1/2 inches apart. Repeat until you have about 36 cookie balls.
Place the sheet pan in the oven and bake for up to 15 minutes until a light golden brown, checking at 13 minutes.
Remove the pan from the oven and allow the cookies to cool until you can handle them. Transfer the warm cookies to a wire rack and continue to cool.