Par-cook the potatoes: Bring a pot of salted water to a boil. Add cubed potatoes and simmer 5–7 minutes, until just tender but not falling apart. Drain well and let them steam-dry for a minute. This step helps get that golden, crispy crust.

Heat the skillet: Place a large cast-iron or heavy skillet over medium-high heat. Add 2 tablespoons oil (or 1 tablespoon oil + 1 tablespoon butter) and heat until shimmering.

Brown the potatoes: Add potatoes in an even layer. Don’t stir for 3–4 minutes to allow browning. Season with salt, pepper, paprika, and thyme. Flip and continue cooking 6–8 more minutes, stirring occasionally, until crisp and deeply golden.

Sauté the aromatics: Push potatoes to one side. Add the remaining tablespoon of oil, then the onion and bell pepper. Cook 3–4 minutes until softened and lightly caramelized. Stir in garlic for the last 30 seconds.

Combine and taste: Fold the onions and peppers into the potatoes. Taste and adjust seasoning with more salt, pepper, or paprika. If using cooked bacon or sausage, stir it in now.

Make wells for the eggs: Use a spoon to create 4 small spaces in the hash. Lower heat to medium. Crack an egg into each well. Season the eggs lightly with salt and pepper.

Cook the eggs to your liking: Cover the skillet with a lid. Cook 3–5 minutes for set whites and runny yolks, or longer for firmer yolks. No lid? Add a splash of water and tent with foil to steam.

Finish and garnish: Turn off the heat. Sprinkle with fresh herbs and, if you like, a little cheese. Add chili flakes for heat.

Serve hot: Scoop onto plates and serve with hot sauce, a dollop of sour cream, or a drizzle of pesto.