1. Trim stem end from each Brussels sprout, cut in half lengthwise, then slice each half crosswise into thin ribbons.
2. Warm oil in a 12-inch skillet over medium-high heat until hot but not smoking. Add ham and cook, stirring occasionally, until browned in spots, 3 to 5 minutes. Add sprouts and cook, stirring, until they begin to wilt and turn bright green, about 5 minutes (they will shrink as they cook, so your pan may be full at first).
3. Season sprouts with salt, pepper and mustard; continue cooking and stirring until sprouts are tender but still bright green, about 8 minutes. If they begin to brown, reduce heat. Remove pan from heat, stir in sour cream and serve.