Whisk the eggs and milk together in a bowl until fully combined.

Melt the butter in a non-stick pan over low heat.

Pour in the egg mixture and stir continuously with a spatula over low heat until softly set, being careful not to overcook.

Remove from heat while still slightly wet, then stir through the cream cheese until melted and combined.

Transfer to a blender and pulse until completely smooth, adding a splash of milk if needed.

Season lightly and serve immediately while warm.