Preheat your oven to 375°F (190°C) and line a large baking sheet with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until evenly combined.
In a large mixing bowl, cream together the softened butter, light brown sugar, granulated sugar, and vanilla extract until pale and fluffy. Mix in the large egg until well incorporated.
Add the dry flour mixture to the butter mixture. Fold until just combined, then add the shredded coconut. Do not fully incorporate the flour before adding the coconut.
Scoop large mounds of dough (about 4.5 oz each, or use two scoops from a 2-oz scoop) and place them onto the prepared baking sheet, leaving rustic shapes. Chill for 30 minutes.
Bake for 10 minutes, then reduce the oven temperature to 350°F (175°C) and bake for an additional 3-5 minutes, or until the edges are golden brown and the centers are still slightly soft. Let cool on the baking sheet for 3 minutes before transferring to a wire rack to cool completely.