Heat butter or oil in a 10-12 inch cast-iron skillet over medium heat or hot coals, melting butter if used.
Cook onion and pepper until soft, about 4 to 5 minutes; push aside.
Add hashbrowns in an even layer and press down. Brown without stirring for 6-8 minutes.
Flip sections if needed, or stir and flatten again. Season with paprika, garlic powder, salt, and pepper. Cook another 5–7 minutes.
If using eggs, make four wells and crack an egg into each. Cover with foil or a lid; cook 4–6 minutes until eggs are set.
Sprinkle with parsley; serve from the skillet.