In a bowl, mix the flour, sugar, baking powder, baking soda, and salt. Using a coarse grater, shred the butter in to the flour mixture. Use your fingers to mix the butter in until it resembles coarse meal.
In a separate bowl, whisk the yogurt and the egg together. Using a fork, mix the yogurt mixture into the flour mixture. Use your hands to fold in the fruit until it becomes a dough. It may seem dry, but there is enough liquid to turn it into dough.
On a lightly floured surface, roll out the dough into a circle about 3/4 inch thick. Sprinkle with some sugar and cut the dough into triangles. Place each triangle on a cookie sheet lined with parchment paper. Bake for about 23 to 25 minutes.
For assembly: Slice the scones in half horizontally and pile on the whipped cream, compote, and fresh blackberries. Serve immediately.