Preheat oven to 375 degrees Fahrenheit. Put sugar and lime zest in a large liquid measuring cup and smoosh together with your fingers so the sugar becomes infused with lime. Add milk, lime juice, vanilla extract, and egg; whisk to combine.
Combine flour, baking powder, and salt in a large bowl; whisk to combine. Use a pastry blender or fork to cut in the butter until mixture takes on a sandy texture. Fold in blueberries and coconut. Add milk mixture and stir until just moist. The dough will be pretty sticky at this point.
Turn dough onto a parchment paper lined baking sheet and pat into an 8-inch circle. Cut dough into 10 triangles. Brush with egg white and sprinkle with sugar. Bake for 18 minutes, until golden. Serve warm and drizzled with lime glaze.
To make the lime glaze, whisk powdered sugar and lime juice together. Add milk a little bit at a time until you reach the consistency you like.