Line a large, rimless baking sheet with parchment paper and set aside. Preheat oven to 400 degrees.

In large bowl, whisk together flour, sugar, baking powder, baking soda, and salt. Use the largest holes on a box grater to grate in cold butter. In separate bowl, whisk buttermilk with egg. Pour over flour mixture. Stir with fork to make a soft, ragged dough.

Dump it out onto lightly-floured surface and scatter mango and white chocolate over top. Gently fold the dough over itself a few times to incorporate the add-ins and make a cohesive dough, then press it into a 10 x 7-inch rectangle log. Cut crosswise to make 6 triangles. Place on prepared pan. Bake in center of oven until golden, 15-18 minutes. Transfer to rack and let cool.