Preheat oven to 375 degrees F. Line a baking sheet with parchment; set aside. In a large bowl combine all-purpose flour, whole wheat flour, baking powder, sugar, baking soda, and salt. Using a pastry blender or two knives, cut in butter until mixture resembles coarse crumbs. Stir in cheese, ham, and dill. Combine sour cream, egg, and mustard; add all at once to flour mixture. Using a fork, stir just until mixture is moistened, Do not overwork.
Turn dough out onto a lightly floured surface. Knead dough by folding and gently pressing it for four to six strokes or just until dough holds together. Pat or lightly roll dough until 3/4 inch thick. Cut dough with a floured 2-1/2- to 3-inch biscuit cutter. Reroll scraps as necessary, dipping cutter into flour between cuts. Place dough circles 1 inch apart on prepared baking sheet. Bake for 18 to 20 minutes or until golden. Cool slightly on a wire rack. Serve warm. If desired, sprinkle with fresh dill. Makes 10 to 12 scones.