In a large nonstick skillet, heat 1 tablespoon oil over medium heat. Stir in potatoes, 1 teaspoon each salt and pepper. Cover, and cook for 8 minutes, stirring once.
Add remaining 1 tablespoon oil, onion, and bell pepper. Cook, stirring frequently, until soft, about 8 minutes. Add pot roast and pan juices, if using, and cook, stirring occasionally, until heated through, about 7 minutes. Transfer to individual plates; keep warm.
Wipe the skillet with a paper towel, and put pan over medium heat. Crack the eggs into the pan, and cook until the whites are just set, 4 to 5 minutes. Top the hash with the eggs.
Note: Use celery or mushrooms instead of the green pepper, if you prefer. You can also top the hash with tomato sauce rather than eggs.