Heat butter in a frying pan (cast iron preferred) on medium high heat.
Add the onions and cook a couple minutes, until translucent.
Add the corned beef, potatoes, and beets.
Stir in the pan to combine, and spread out evenly in the pan.
Reduce the heat to medium.
Press down with a metal spatula to help brown the mixture.
Don't stir, but just let cook until nicely browned on one side, then use a metal spatula to lift up sections of the mixture and turn over to brown the other side.
If the mixture sticks to the pan too much, just add a little more butter to the pan where it's sticking.
When nicely browned, remove from heat.
Sprinkle in some Worcestershire sauce, if using.
Stir in fresh chopped parsley, if using, and sprinkle on freshly ground black pepper to taste. There should be enough salt from the corned beef, but if not, add salt to taste. Serve plain or with fried or poached eggs.