Melt 1 tablespoon butter in a cast iron skillet (or other heavy, oven-safe skillet) over medium high heat.
Add the sweet potatoes and cabbage. Season with salt and pepper to taste, and stir.
Cook over medium heat, stirring occasionally, until sweet potatoes are fully cooked and cabbage is softened (10-15 minutes).
Remove from heat and stir in remaining 1 tablespoon butter, along with corned beef.
Using a spoon, make four wells in the cabbage mixture. Crack an egg into each one.
Bake for 10 minutes or until whites of egg are set and yolks are still runny (or longer if you want cooked yolks).
Garnish with parsley and serve hot fresh out of the oven.
Don't have an oven proof skillet? Sauté the veggies and corned beef as directed, then transfer to a large baking dish. This will accommodate 8-10 eggs and more veggies if needed, to serve a crowd.
Make it vegetarian: simply omit the corned beef (you could use a vegetarian bacon or other “meat” as a substitute, if you want to).
Make it paleo: use ghee instead of butter.
Use leftover corned beef and cabbage from the classic St. Patrick's day meal to make this! Just add the cooked cabbage with the corned beef after the sweet potatoes have finished cooking.
The provided nutrition information does not include any added sodium from seasoning to taste, any optional ingredients, and it does not take brands into account. Feel free to calculate it yourself using this calculator or by adding the recipe to Yummly.