Prep. Coarsely chop the onion. Chop the meat and potatoes into 1/4 to 1/2" cubes.
In a large bowl, beat 2 of the eggs and the thyme with a fork, then add the broth, beat some more, then the corned beef, potatoes, and onions. Stir and let it sit for about 5 minutes so the dry meat will absorb the liquid.
Fire up. On your grill or a side burner, preheat a frying pan, preferably a cast iron pan.
Cook. Add the fat to the pan. Roll it around so it coats the bottoms and sides. Add the hash mix and pat it down with a spatula. Cover and cook about 5 minutes, then with a spatula, turn things over.
Crack the remaining eggs and lay them on top of the hash. Cover and cook until the whites have set but the yolks are the way you like them. Food safety experts say that if you are not using pasteurized eggs you should cook them until the yolks are set. Be careful don't burn the bottom of the hash. If the bottom is dark brown and the eggs are not done, add a few ounces of water to make steam and put the cover on.
While the eggs are cooking, heat the leftover cabbage as a side dish. Microwave is fine.
Serve. Plate the corned beef hash and eggs and serve immediately.