Pour enough water into large roasting pan to reach a depth of 2 inches. Pour enough water into a large skillet to reach a depth of 1-½ inches; add 1 teaspoon salt to skillet and bring to a simmer.
Crack each egg into a separate custard cup. Working with 4 eggs per batch, gently slide 1 egg at a time into simmering water in skillet. Cook just until egg whites are set, about 1 minute (yolks will be only partially cooked).
Using a slotted spoon, carefully transfer eggs to prepared roasting pan with water. Reserve skillet with water.
Chop leftover vegetables (onions, carrots, potatoes, cabbage) roughly and place in a large bowl. Any leftover vegetables will do.
Chop leftover corned beef and add to bowl. Season to taste with salt and pepper.
Add two eggs that have been lightly beaten to the bowl to help bind the ingredients together. If you have any leftover broth, add a tablespoon or so to the bowl. Mix all the ingredients together.
Separately, in a large frying pan over medium-high heat, add oil and sauté onion until softened, about 5 minutes.
Then add corned beef hash mixture to the pan and cook until golden brown on bottom, occasionally pressing down with spatula, about 4 minutes. Turn hash over in small portions and cook until second side is golden brown, occasionally pressing down with spatula, about 3 more minutes.
Bring water in reserved skillet to a simmer. Using a slotted spoon, gently transfer poached eggs from roasting pan back to skillet. Cook just until yolks are softly set, about 2 minutes.
Divide hash among plates. Top with one or two poached eggs and serve. Add diced scallions if desired. Season to taste with salt and pepper.
Enjoy nice and hot!