Place the potatoes in a colander, lightly salt them and let drain for a few minutes.
In a large nonstick skillet, melt the butter over medium heat. Mix in the potatoes, carrots and corned beef and increase the heat to medium-high. Set a plate on top and weight it down with a heavy can. Stir in the crust that forms about every 5 minutes. Cook until the potatoes are tender, about 15 minutes. Stir in the cream and turn off the heat. Season to taste with pepper.
Top the hash with the cooked eggs and serve with the toast.