Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat. In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.
In a large mixing bowl, use an electric mixer to beat the softened butter, granulated sugar, and brown sugar together until the mixture is light and fluffy — about 2 to 3 minutes.
Add the egg and vanilla extract to the butter-sugar mixture. Beat until fully combined and smooth.
Gradually add the dry flour mixture to the wet ingredients, mixing just until combined. Avoid overmixing to keep the cookies tender. Fold in the shredded coconut gently using a spatula.
Using a cookie scoop or tablespoon, drop rounded spoonfuls of dough onto your prepared baking sheet, spacing them about 2 inches apart. Bake for 10-12 minutes, or until the edges are lightly golden but the centers still look soft. Remove from oven and allow cookies to cool on the baking sheet for 5 minutes before transferring to a cooling rack.
While the cookies cool, puree your ripe mango in a food processor or blender until smooth. In a medium bowl, beat the softened cream cheese and powdered sugar together until creamy. Gently fold in the mango puree until fully combined and smooth.
Once the cookies are completely cool, spread about 1 to 2 tablespoons of the mango cream filling onto the flat side of one cookie. Top with another cookie, pressing gently to sandwich the filling without squeezing it out. Repeat with all cookies.
For best results, refrigerate the assembled sandwich cookies for at least 30 minutes to let the filling set. This also makes them easier to handle when serving.