Preheat the oven to 400 degrees F (200 degrees C). Grease a baking sheet.
Make the scones: Sift flour, baking powder, sugar, and salt into a large bowl. Cut in butter with a pastry blender or by rubbing between fingers until lumps are the size of peas. Stir in currants.
Whisk milk and sour cream together in a measuring cup; gently stir into flour mixture until dough is moistened, being careful not to overwork the dough.
With floured hands, pat dough into 2- to 3-inch diameter balls. Place onto the prepared baking sheet and flatten lightly. Scones should slightly touch each other.
Make the egg wash: Whisk egg and milk together. Brush the tops of scones with egg wash and let them rest for about 10 minutes.
Bake in the preheated oven until the tops are golden brown, 10 to 15 minutes.