Preheat an oven to 425F.
In a large mixing bowl combine the baking mix, sugar, chopped ham, about 1/2 cup of the shredded cheese and the chives. In a small bowl, combine the egg and milk. Pull out about a teaspoon of the liquid in a small dish or coffee cup then add the remaining liquid to the bowl of dry ingredients. Give it a gentle stir with a fork or rubber spatula until a soft dough forms.
Sprinkle a little bit of baking mix onto your worktable and turn the dough out onto it. Give it a quick knead, about 10 turns should do the trick. Transfer the dough to a baking sheet and use your hands to shape it into a round that is flat on top and about 8 inches across. Brush the reserved liquid over the top of the dough and top with the remaining cheese. Cut into 8 wedges with a long knife. Leave the wedges together, though, you'll break them apart after they've finished baking.
While the scones are baking, combine the softened butter and mustard in a medium-size mixing bowl. Set aside until the scones are ready.
Pop the pan into the oven and bake the scones until the edges are golden brown, 12-15 minutes. Remove from oven and let sit for about 5 minutes. Break the wedges apart and serve the scones with the mustard butter alongside.