Preheat oven to 400˚F (200˚C). Line a large baking sheet with parchment or lightly grease.
In a large bowl, combine the flour, baking powder, and salt.
Quickly cut in the butter using a dough blender, two forks, or your fingers until blended and no pieces are larger than a pea.
Fold in the finely chopped fresh basil and shredded Parmesan.
In a small bowl, beat together the egg and heavy cream.
Pour into the dry ingredients and gently combine just until the mixture comes together. Do not overmix. If the mixture continues to fall apart, add a little more cream.
Place the dough on floured surface and lightly knead to bring it together. Gently press into a disc about 3/4 inch (2 centimeters) thick.
Cut the disc into 6 equal slices. Transfer to the prepared baking sheet about 1/2 inch (1.25 centimeters) apart.
In a small bowl, whisk together the egg yolk and cream. Brush over the top of each scone. Take care to not brush the sides. Sprinkle with the shredded Parmesan cheese.
Bake in preheated oven until puffed and golden, 12-15 minutes.
Allow the scones to cool on the pan for 5 minutes before removing to wire rack.