Preheat the oven to 425 F and line baking sheets with parchment paper.
In a large bowl, stir together the flour, sugar, baking powder, baking soda, cayenne pepper, and salt.
Using a pastry blender or two knives, cut in the butter until the mixture resembles coarse crumbs.
Stir in the cheese and dill.
Add the buttermilk all at once, stirring with a fork to make a soft, sticky dough.
With lightly floured hands, press the dough into a ball.
On a lightly floured surface, knead gently 10 times.
Pat out the dough into a 3/4-inch thick round.
Using a 2-1/2-inch floured cutter, cut out rounds. Place on a baking sheet.
Gather up the scraps and repeat; cut out more rounds. Brush the tops of the scones with egg.
Bake in the oven for 12 to 15 minutes or until golden.