Heat butter or oil in a large skillet over medium heat. Add the diced potatoes and cook, stirring occasionally, until they start to brown and crisp up (about 8-10 minutes).
Sauté the Aromatics
Add the diced onion and bell pepper to the pan. Cook until softened, about 3-4 minutes. Stir in the minced garlic and cook for another 30 seconds.
Add the Brisket
Toss in the chopped brisket, smoked paprika, black pepper, salt, and cayenne (if using). Stir everything together and cook for another 5 minutes, allowing the brisket to crisp up slightly.
Fry the Eggs
While the hash finishes cooking, fry eggs in a separate pan to your desired doneness.
Serve and Enjoy
Plate the hash and top with a fried egg. Garnish with fresh parsley or green onions, and drizzle with hot sauce or barbecue sauce if desired.