Place the potatoes in a microwave-safe bowl with the salt and pepper and stir. Cover the bowl with plastic wrap and microwave on high power for 6 minutes or until tender. Preheat the oven to 400 degrees.
Whisk together the eggs, cream, and mustard.
Heat the oil in a cast iron skillet over medium heat until it begins to shimmer. Add the onion and cook until tender and translucent, about 5 minutes. Add the potatoes and corned beef. Pour the egg mixture over top and use a spatula to make sure the eggs surround the potatoes and corned beef. Cook for 1 minute on the stove, then transfer the pan to the oven. Cook for 12-14 minutes or until the eggs are fully set. Top with chives.
Let cool for 5 minutes before cutting into wedges to serve.