How to Make It
Preheat the oven to 350°. In a large ovenproof skillet, heat 1 tablespoon of the oil. Add the ham and cook over moderately high heat, stirring, until lightly browned, about 2 minutes. Add the onion and cook for 1 minute. Add the sweet potatoes and thyme, season with salt and pepper and cook just until the sweet potatoes are lightly browned in spots, 2 to 3 minutes. Add the vermouth and cook, scraping up any browned bits. Roast the hash in the oven for about 20 minutes, until the potatoes are tender. Stir in the duck and scallions and roast until heated through, about 5 minutes; keep warm.
Heat the remaining 1 tablespoon of oil in a large skillet. Working in 2 batches, fry the eggs over-easy over moderate heat, about 3 minutes. Transfer the hash to shallow bowls, top with the fried eggs and serve with hot sauce.