Slice potatoes wafer thin, using vegetable slicer or food processor. Drop potato slices into cold water to avoid discoloration.
Rub rosemary between fingers to break apart. Heat oil in a 12-inch cast iron skillet. Add potatoes, and cook over medium-high heat, shaking pan gently to toss but not break potatoes. When potatoes are slightly limp, sprinkle with rosemary, mustard, and pepper. Shake well to mix. Press with spatula. Cook until potatoes are brown and crisp on bottom, lifting carefully to check.
Sprinkle cheese on top of the potatoes. Immediately place skillet in oven and bake 2 to 3 minutes or until cheese starts to bubble and brown slightly.