Fill a medium bowl with cold water. Fill a heavy deep pot with oil and heat to 390 degrees F. Slice potatoes into paper thin slices, about 1/8-inch thick, using a mandoline. As potatoes are sliced, immediately place them in the water to prevent color change. When done, remove potatoes from water in batches and blot dry on paper towels. Carefully add potatoes to oil making sure that aren't stuck together. Cook potatoes, gently stirring with tongs or a strainer, until golden brown and crispy, about 3 to 4 minutes. Remove to a paper towel-lined sheet pan and immediately sprinkle with a pinch of the sea salt and pepper and 1 teaspoon Gruyere. Check oil temperature and repeat with the remaining potatoes until all are cooked.
Serve immediately with French Onion Dip or allow them to cool completely and store in an airtight container for up to 2 days.