Remove the skin from the eel. Carefully remove fish flesh from the bone and cut into long pieces. Preheat oven (electric cooker: 125 °C/circulating air: 100 °C/gas: see manufacturer). Brush the slices of bread with 1 teaspoon of butter each.
Wash the chives, shake dry and cut into small rolls. Thickly sprinkle breads with it.
Wrap the eel in baking paper and warm it up in a hot oven for about 5 minutes. In the meantime whisk eggs and season with salt and pepper. Heat 1 tsp. butter in a coated pan. Pour in the eggs, let them falter slightly over a low to medium heat and scramble them together to form scrambled eggs.
Spread the scrambled eggs on the breads, cover with eel.