I have two very big Duck eggs - what should I do with them?

Oh man, duck egg pasta dough is awesome.
But if you want to showcase them a little more, just toss the yolks with some pasta (as you would carbonara) with some pecorino/or parmigiano (pecorino boschetto would be really nice). The yolks of duck eggs are where it's at, the whites..not so much.

That, or cure the yolks and shave them on stuff.

Duck eggs make lovely custard and ice cream. Their big colorful yolks make these dishes intensely yellow. I've also been known to cook one just shy of hardboiled and eat it for lunch with Japanese Kewpie mayo on top. I'll be following this thread, as my three Khaki Campbells are in full production, and I have a refrigerator full of duck eggs. (Ducks lay their eggs at night, by the way. In the daytime, they're busy eradicating slugs and ticks.)

I get big duck eggs from a neighboring farmer--beautiful dark yellow and rich enough to make a single serving from each one. Diana Kennedy once said that duck eggs make the finest cake, much better than chicken eggs. I haven't tried but what I often do is steam bitter spring greens, then braise them in extra-virgin olive oil with a chopped garlic clove and a pinch of chili. Fry the eggs gently, also in evoo, so the yolks are still a bit runny, then top each serving of greens with a duck egg which looks mighty pretty and, when broken, makes a luscious sauce for the greens.

Since you want to poach and put on top of something, how about on top of a burger? I love burgers topped with a fried egg. Great for dinner or breakfast.

You might also like putting the eggs on top of creamy polenta. My favorite cafe does this for their brunches with a variety of topping like bacon, blue cheese and a drizzle of maple syrup or pulled pork.

I've also had a frisee salad with a little chevre and an egg on top as my meal.