Prep. If using the eggs, preheat the oven to 400˚F.
Heat the oil and butter. Heat the olive oil and the butter in a large skillet, preferably a cast iron skillet.
Saute the aromatics. To the heated oil, add the onions and cook for 2 minutes, occasionally stirring. Then, stir in the garlic and cook for 15 seconds.
Cook the potatoes. Add the diced potatoes, season them with salt, pepper, oregano, and basil; cook over medium-high heat for 15 minutes, or until slightly browned and tender. Stir occasionally.
Add the cubed corned beef. Stir in the corned beef and the worcestershire sauce; cook for 5 more minutes or until crispy. Remove from heat.
Continue if using the eggs and make 4 to 6 wells in the hash. Crack an egg into each well. Season the eggs with salt and pepper.
Bake. Put the skillet in the oven and bake for about 8 to 10 minutes, or until the egg whites are set.
Finish and serve. Remove the hash from the oven, garnish with parsley, and serve.