Boil the diced potatoes until tender, about 10 minutes.
Drain the potatoes and set them aside to cool slightly.
In a large skillet, heat olive oil over medium heat.
Add the diced onion and carrots; sauté until softened, about 5 minutes.
Stir in the cooked corned beef and cook for another 5 minutes.
Add the cooked potatoes to the skillet; mix everything well.
Press the mixture down into the skillet and let it cook undisturbed for 5-7 minutes.
Flip the hash and cook for an additional 5 minutes until crispy.
Season with salt and pepper to taste.
If desired, top with fried eggs before serving.