Place the sweet potatoes in a pot large enough to fit them, and cover with water by 2 inches. Add 2 tablespoons salt. Bring to a boil, then boil the sweet potatoes until tender, about 15 minutes. Scoop the flesh into a food processor and puree. Portion out 10 ounces, then set aside in the fridge to cool (use the remainder for another use).
Melt the butter in a small pot over medium heat. Add the flour and cook for 2 minutes to make a roux. Whisk in the warm milk, then season with the nutmeg and some salt and pepper. Cook until thick, about 3 minutes, then remove from the heat. Set the bechamel aside to cool completely to room temperature.
Generously brush four 12-ounce ramekins with butter. Grind the chips in a food processor together with 1/2 cup Parmesan. Reserve 1/2 cup of the chip mixture. Generously coat each ramekin with the remaining chip mixture, tapping out any excess.
Preheat the oven to 375 degrees F. Arrange the prepared ramekins on a sheet pan.
Beat the egg whites to stiff peaks. Fold together the bechamel, egg yolks and sweet potato puree. Fold in the remaining 1/4 cup Parmesan. Fold in half of the egg whites until evenly combined, then fold in the remaining egg whites, being careful not to overwork. Divide the mixture among the ramekins, filling each three-quarters of the way. Sprinkle with the remaining chip mixture and bake until the centers are tender and warmed through, 35 to 40 minutes. Serve immediately.