Cook the corned beef according to the package directions. You want to make sure that it is fork tender.
Remove the corned beef from the oven and cool in the refrigerator overnight, or until it is cool enough to handle and dice without crumbling the pieces.
Bake your potatoes in the oven, or microwave which ever you prefer. Slice and cool in the refrigerator along with the corned beef.
When the corned beef and potatoes are cooled dice them in a 1/4-inch dice.
Dice the peppers and onions in a 1/4-inch dice too.
When you have all the ingredients ready to go, heat the olive oil and butter in a large skillet over medium heat.
Add the diced potatoes, corned beef, peppers, and onions and season with salt and pepper.
Cook until the peppers and onions are soft, stirring occasionally so that the bottom doesn't burn, but develops nice brown crusty pieces.
Some people like their hash extra crispy, cook until it is the desired texture you prefer, watching carefully so you do not burn the hash.