Heat 2 tablespoons of butter in a large cast iron skillet, over medium-high heat. Add the onion and cook until softened and starting to brown, about 3 minutes. Then, add the garlic and cook until fragrant, 1 minute.
Add the shredded corned beef and cook, stirring occasionally, until slightly browned, about 5 minutes. Remove with a slotted spoon and reserve.
Melt the remaining butter and add the diced potatoes, spreading them into a single even layer. Cook - stirring often - until tender and golden brown, 15-20 minutes.
Returned the corned beef and onion mixture to the skillet. Stir to combine and season with salt and pepper. Cook, undisturbed, until crispy and browned on the bottom. Flip the hash in sections until the bottom becomes the top.
Pour the heavy cream on the edges, letting it run down to the bottom of the skillet. Continue cooking until browned and crispy on the other side.
Taste and adjust seasoning as needed.
Heat the oil in a large non-stick skillet, over medium heat. Break the eggs, one by one, into a small bowl. Carefully add the eggs to the fully heated pan and let it cook until the whites are completely set and the yolks are done how you like them. (see notes)
Top the corned beef hash with the eggs, drizzle with chili oil and garnish with chopped parsley.
Serve immediately!