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.
Note: Nutritional analysis is per scone.