Brush or spray the potato halves with vegetable oil. Grill over Direct Medium heat until tender when pierced with a fork, 30 to 35 minutes, turning three or four times during grilling time. Remove from the grill and allow to cool slightly.
When cool enough to handle, use a small sharp knife to cut around the cut side of the potato to within 1/4 inch of the skin. Using a teaspoon or melon baller, scoop out the interior of the potato, leaving a 1/4-inch-thick shell attached to the skin. Place the potato pulp in a large bowl. Set the potato shells aside while preparing the stuffing.
TO MAKE THE STUFFING:
Using a potato masher or pastry blender, mash the potato pulp. Add the sour cream and milk and mix well. Stir in the ham and half of the cheese. Add the mustard and season with salt and pepper. Mix well. Adjust the seasoning with more mustard, if desired. Divide the stuffing evenly among the skins so the stuffing mounds slightly. Sprinkle the remaining cheese over the stuffing.
Grill the stuffed potatoes over Direct Medium heat until the cheese is melted and the potatoes are heated through, about 10 minutes. Serve immediately.
Note: Try a Cheddar & Bacon version, or Blue Cheese and Chives.