Slice potatoes wafer thin, using vegetable slicer or food processor, dropping them into cold water to avoid discoloration. Rub rosemary between fingers to break leaves and reserve.
Preheat oven to 425°F. Heat oil in 12-inch cast iron skillet. Add potatoes; cook over medium-high heat, shaking pan gently to toss but not break potatoes. When potatoes are slightly limp, sprinkle with rosemary, mustard to taste and pepper. Shake well to mix. Press with spatula. Cook until brown and crisp on bottom, lifting carefully to check.
Sprinkle with cheese. Immediately place skillet in oven. Bake 2 to 3 minutes until cheese starts to bubble and brown.
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