Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper. Chop dried mango into small chip-sized pieces and set aside.
Beat softened butter, granulated sugar, and brown sugar together on medium-high speed for 3–4 minutes until light, fluffy, and pale. Scrape down the bowl halfway through.
Reduce speed to medium and add eggs one at a time, beating 30 seconds after each. Mix in vanilla and coconut extracts until smooth and glossy, then scrape down the bowl.
In a separate bowl, whisk together the flour, baking soda, and salt for about 30 seconds to evenly distribute the leavening.
With the mixer on low, gradually add the flour mixture to the wet ingredients and mix just until no streaks of flour remain — about 30–45 seconds. Do not overmix.
Remove the bowl from the mixer and fold in the shredded coconut, chopped dried mango, and white chocolate chips using a rubber spatula until evenly distributed.
Scoop dough into 2-tablespoon balls and place 2 inches apart on prepared baking sheets, about 12 per sheet. If dough is too soft, refrigerate for 15 minutes before scooping.
Bake for 10–12 minutes, rotating pans front-to-back and switching racks at the 6-minute mark. Remove when edges are golden but centers still look slightly underdone.
Let cookies rest on the baking sheet for 5 minutes to set, then transfer to a wire rack to cool completely, about 20–30 minutes. Texture will firm up as they cool.