In a large frying pan, melt the butter over medium-high heat.
Crack the duck eggs into the pan. Cook like you would chicken eggs, frying the bottoms up. If wanted, steam them by adding 2 tablespoons of water to the pan and placing a lid on top. I find that this cooks the top of the eggs without having to actually flip them over, thus you won't break the yolk.
Steam the eggs until the tops are white colored but the yolk is still wobbly enough to dip toast in. Alternately you can cook them until well done if you don't like yolky eggs.
IF you want to scramble them, melt the butter then add in the cracked duck eggs. Mix and cook until done.