Preheat oven to 400°. In a large bowl, combine flour, mustard, baking powder, and salt. With your fingers or a fork, work butter into flour mixture until it resembles cornmeal studded with a few pea-size pieces. Stir in cheeses, chives, and dill.
Add milk and stir to combine. Transfer dough to a floured surface and gently knead 2 or 3 times until it comes together. Pat into a 1-in.-thick disk and cut into 8 triangles. Arrange triangles about 2 in. apart on a baking sheet. Bake until golden brown and cooked through, 20 minutes.
These are incredibly easy and tasty. They are actually the first scones I ever made and now I'm addicted. I first made them for a work event and they won rave reviews from even some of the harshest food critics in my office. I did make one slight modification; instead of using grated cheese, I use high-quality (somewhat thick) slices of extra sharp cheese from the deli counter and "chopped" them up into tiny squares. I primarily did this out of the necessity the first time I made them because it was the only cheese I had on hand but when they turned out so well, I permanently adopted the approach. I like getting slightly larger chunks of cheese in every bite as opposed to the shreds that kind of get lost in the mix.