Par-cook the potatoes: Place the cubed potatoes in a pot, cover with cold, well-salted water, and bring to a gentle boil.
Simmer 5–7 minutes until just tender when pierced, not falling apart. Drain well and let steam off for a minute to dry.
Preheat the skillet: Set a 10–12 inch cast iron skillet over medium heat and warm 2 tablespoons of olive oil until shimmering. Proper preheating helps prevent sticking and promotes a golden crust.
Build the flavor base: Add the onion and bell pepper.
Season with a pinch of salt and cook 5–6 minutes, stirring occasionally, until softened and lightly browned. Stir in the garlic, smoked paprika, thyme, and red pepper flakes; cook 30 seconds until fragrant.
Crisp the potatoes: Add the drained potatoes and the remaining 1 tablespoon of oil. Spread them into an even layer.
Let them cook undisturbed for 3–4 minutes to develop color, then stir and repeat. Continue until the potatoes are deeply golden and crisp on multiple sides, 8–12 minutes total. Season with salt and black pepper.
Create egg wells: Use a spoon to make 4–6 small wells in the potatoes.
Reduce heat to medium-low to prevent scorching.
Add the eggs: Crack one egg into each well. Sprinkle a touch of salt and pepper over the eggs. Cook uncovered until the whites are mostly set with jiggly yolks, about 4–6 minutes.
If the tops need help setting, cover the skillet for the last minute or two or slide the skillet under a low broiler briefly. Keep an eye on it—you want set whites and runny yolks.
Finish and serve: Remove from heat. Sprinkle chopped parsley or chives over the top.
Add optional toppings like feta, green onions, or hot sauce. Serve straight from the skillet with toast or a side salad.