In a large bowl, whisk together the flour, sugar, baking powder, salt, and black pepper. Stir in the fresh dill and chives.
Using a pastry blender or two forks, cut in the cold, cubed butter until crumbly and mixture resembles small peas. Carefully stir in the feta, just until incoporated.
Pour the 1 cup of cream into the mixture, stirring only until the dry ingredients have moistened and mixture holds together when pressed. Carefully knead into a ball.
Transfer dough ball to a lightly floured surface. Gently press dough into an 8-in circle. Cut into 8 wedges. Place wedges onto a parchment lined sheet tray, leaving about 1-inch between each. Place tray into the refrigerator and allow to cool for about 20 minutes.
While scones are in the refrigerator, preheat the oven to 425° F. In a small bowl, whisk together the egg and 1 tablespoon of cream. After 20 minutes, remove the tray of scones from the refrigerator. Brush each scone with the prepared egg wash (you will probably not use all of it.)
Bake scones for about 18 to 20 minutes, or until tops are golden. Allow the scones to cool slightly before eating.