Begin by chilling the can of corned beef in the refrigerator for at least 30 minutes. This makes it much easier to handle and dice.
Once chilled, open the can and carefully remove the corned beef. Dice it into small, bite-sized cubes. You can also mash it slightly with a fork if you prefer a less chunky texture.
Heat the olive oil or butter in a large non-stick skillet over medium-high heat. Add the chopped onion and bell pepper (if using) and sauté until softened and lightly browned, about 5-7 minutes.
Add the diced or mashed corned beef to the skillet. Cook, stirring occasionally, until it begins to brown and crisp up, about 5-8 minutes. Break it apart with your spatula as it cooks.
Stir in the diced cooked potatoes and black pepper. Continue to cook, stirring and pressing down gently with the spatula to encourage browning, for another 8-10 minutes, or until the potatoes are heated through and slightly crispy.
Stir in the fresh parsley and season with salt to taste. Remember that canned corned beef can be salty, so taste before adding too much salt.
Serve immediately, with optional Worcestershire sauce or hot sauce if desired.