In a medium saucepan over medium heat, melt the unsalted butter. Continue cooking, stirring frequently, until the butter turns golden brown and gives off a nutty aroma. Remove from heat and let it cool slightly.
In a large mixing bowl, combine the browned butter, granulated sugar, and light brown sugar. Whisk together until smooth. Add the egg and vanilla extract, mixing until well incorporated.
In another bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add the dry mixture to the wet mixture, stirring gently until just combined.
Fold in the sweetened shredded coconut and white chocolate chips, ensuring they are evenly distributed throughout the dough.
Cover the dough with plastic wrap and refrigerate for at least 30 minutes. This helps the flavors meld and prevents the cookies from spreading too much while baking.
Preheat your oven to 350°F (175°C). Line your baking sheet with parchment paper.
Using a cookie scoop, portion out the dough onto the prepared baking sheet, leaving space between each cookie. Add a few extra white chocolate chips on top of each dough ball for a beautiful presentation.
Bake the cookies for 10-12 minutes, or until the edges are lightly golden. The centers may look slightly underbaked, but they will continue to cook on the baking sheet once removed from the oven.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely. Enjoy your Coconut White Chocolate Cookies with a cold glass of milk or a cup of tea.