Make the mustard cream sauce. Mix ingredients together in a small bowl. Cover and refrigerate.
Make the hash. Preheat oven to 325 F. Heat a 12-inch skillet over medium heat, about 5 minutes. Add butter and olive oil. Add half the potatoes in a single layer, seasoning with ½ teaspoon salt.
Cook for 4 minutes undisturbed. Turn and continue to cook until golden brown on all sides, about 6 more minutes. Remove from skillet to a paper towel lined plate and repeat with remaining potatoes, adding more oil and butter as needed.
Mix onion and bell pepper in the skillet and cook for 5 to 7 minutes until the onion is translucent. Use a little more oil if needed. Add pepper, paprika, thyme, garlic, and corned beef, cooking for 5 minutes more. Return potatoes to the pan and mix well.
Make 4 wells in the hash and crack in the eggs, working carefully to not pierce the yolk.
Bake until the whites are set and the yolks are at your desired doneness, about 8 to 10 minutes.
Remove from oven, season with salt and pepper to taste, drizzle with mustard cream sauce and top with chopped parsley.
