Crack the turkey eggs into a large mixing bowl.
Add the milk or single cream, season with a pinch of salt and some freshly ground black pepper, then whisk briskly until well combined and frothy.
Heat a non-stick frying pan over a medium–low heat.
Add the butter and let it melt until it starts to foam, then tilt the pan to coat the base of the pan.
Pour in the egg mixture and leave it, undisturbed, for about 30 seconds, until the edges begin to set.
Using a heatproof spatula, gently push the set edges towards the centre, tilting the pan to allow the runny egg to flow underneath. Continue folding and pushing until the eggs are mostly set but still moist and glossy, about 3–5 minutes.
Remove the pan from the heat (the residual heat will continue cooking the eggs) and transfer them to serving plates.
Garnish with chopped fresh chives or parsley, if you like, and serve immediately.