Heat your oven to 450°F. Pour the melted salted butter into a 9x9-inch metal or glass baking pan, ensuring it covers the entire bottom.
In a large bowl, whisk the flour, sugar, baking powder, and salt. In a separate measuring cup, whisk the cold buttermilk and sour cream together until smooth.
Pour the buttermilk mixture into the dry ingredients. Use a spatula to fold until just combined. The dough will be very wet and soggy. Gently fold in the fresh blueberries, taking care not to burst them.
Plop the dough directly into the pan on top of the melted butter. Use a spatula to gently spread it to the edges. It will look like it is "swimming" in butter—this is correct.
Sprinkle the turbinado sugar evenly over the top of the raw dough.
Use a bench scraper or a knife to "score" the dough into 9 squares before baking. This allows the butter to bubble up into the cracks.
Bake for 22-26 minutes. The tops should be a deep golden brown, and the butter should be mostly absorbed.
While the biscuits cool for 5 minutes, whisk the icing ingredients together until thick yet pourable. Drizzle generously over the warm biscuits. Serve.