In a large pot, bring 1 quart of water to a boil.
Peel and chop the potatoes into small, bite sized pieces (about 1/2 inch.) Place them in the boiling water and boil 3-5 minutes, until just fork tender. Drain and set aside.
In a large skillet, heat the butter and olive oil over medium heat. Add the onion, green pepper, and half of the salt & pepper. Sauté until tender, about 5 minutes.
Add the potatoes and the remaining salt & pepper to the skillet. Spread the mixture into an even layer and sauté until potatoes are browned on one side, then flip and cook to brown the other side.
Add the chopped corned beef to the skillet; stir and sauté until heated through.
Garnish with fresh parsley. Top with fried eggs (optional.)