Preheat oven to 375 degrees; line a baking sheet with parchment paper.
Combine dry ingredients in a large bowl. Cut in butter with a pastry blender or fork until pea sized.
Stir in Cheddar and chives, then add buttermilk and 2T water. Knead gently until well blended.
Turn dough out on a lightly floured work surface (it's sticky!) and pat (with floured hands) into an 8" square.
Cut into 2" squares and then each square to a triangle.
Arrange on baking sheet spacing 1" apart.
Brush tops with egg/milk mixture and bake about 25 minutes; until golden.