In a jug, lightly whisk together the eggs and milk, then season. Heat the oil in a non-stick frying pan over a medium heat.
Pour in the eggs and leave to set for 30 seconds. Use a spatula to stir the eggs slowly, for about 2-3 minutes, until the eggs look silky and not completely set.
Remove from the heat and stir in the parmesan, then season with black pepper. Serve on toasted bread and sprinkle with chives and parmesan shavings.