Into a bowl sift the flour, the baking powder, the salt, and the cayenne.
Add the butter and blend the mixture until it resembles coarse meal.
Add the Cheddar and the chives and toss the mixture to combine it.
Stir in enough milk to form a dough and gently knead the dough on a lightly floured surface until combined.
Pat the dough into a round 3/4 inch thick and with a 3-inch round cookie cutter stamp out rounds.
Reform the scraps into dough and stamp out the remaining rounds.
Arrange the rounds on a greased baking sheet, brush them with the egg wash, and bake them in a preheated 425° F. oven for 12 to 15 minutes, or until they are golden.