Break the duck eggs into a large bowl, season with salt and freshly ground black pepper and whisk together well.
Melt the butter in a pan before adding the whisked duck eggs. Cook slowly, stirring occasionally with a wooden spoon, until cooked to your liking.
Add the chopped chives and stir in the cream.
Line four large ramekins with cling film and place the smoked eel pieces into the bases of them. Divide the scrambled egg among these ramekins and leave to stand for one minute.
To serve, turn the ramekins upside down onto plates before removing the ramekins and cling film. Garnish with a little wilted spinach.