Rinse the diced potatoes under cold water until the water runs clear to remove excess starch.
Microwave the potatoes in a covered bowl with a splash of water for 3–4 minutes, or simmer in salted water for 5 minutes, until just tender at the edges. Drain and pat dry.
Heat the skillet over medium-high. Add the olive oil and butter until sizzling.
Spread the potatoes in a single layer. Do not stir for 3–4 minutes to develop color.
Flip in sections and continue cooking 4–6 minutes, seasoning with salt and pepper, until golden and crisp on most sides. Push to the edges of the pan.
Add a drizzle of oil to the center of the skillet. Add the onion and bell peppers.
Cook 4–5 minutes, stirring occasionally, until softened and lightly browned.
Add the garlic, smoked paprika, cumin, and crushed red pepper. Cook 30 seconds until fragrant.
Fold the potatoes back into the veggies. Taste and adjust salt and pepper.
Use a spoon to make 4–6 small wells in the hash. Crack an egg into each well.
Reduce heat to medium. Cover the skillet.
Cook 4–6 minutes for soft, runny yolks, or 7–9 minutes for set yolks. Check at 4 minutes so you don’t overcook.
Sprinkle cheese during the last minute if you like.
Top with chopped parsley or chives.
Serve hot with hot sauce or salsa. Add toast or warm tortillas if you want to stretch it.
