Crack the eggs into a medium bowl. Add the milk, season with a pinch of the Parmesan and add 1 tablespoon of the truffles. Whisk together.
Heat the oil in a medium nonstick skillet over medium heat and swirl it around to coat the bottom of the pan. Add the eggs and let them set for a bit. Using a rubber spatula, lift the sides of the eggs so the uncooked eggs can move underneath the set eggs. Continue cooking until the eggs are just set. Top with the remaining truffles and Parmesan.