Pre-heat the oven to 400 degrees. Melt butter in a large skillet over medium heat. Add the onions and garlic and cook until translucent. About 4-5 minutes.
Reduce the heat to medium-low and add the potatoes, thyme and oregano. Season with pepper
Allow the potatoes to cook, stirring occasionally for about 20-25 minutes or until the potatoes are soft.
Add the corned beef, apples and mushrooms. Turn the heat back up to medium and allow to cook for another 5 minutes, stirring frequently.
Using a spoon, create 2 - 4 holes, depending on how many eggs you want, in the hash mixture for the eggs. Crack one egg into each hole.
Transfer to the oven and bake until the egg whites set, about 8-10 minutes. Season with salt and pepper and top with the parsley.
Notes
You can also fry eggs on the side and top the hash with eggs during plating.