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Heat 2 tablespoons of the oil in a 10-inch or larger cast iron skillet until shimmering.
Add the onion and pepper, and cook, stirring occasionally, until soft, about 5 minutes.
Add the sweet potatoes, paprika, coriander, pepper, and 1 teaspoon of the salt.
Cook, stirring occasionally, until almost tender but there's still slight resistance when pierced with a fork, about 8 minutes.
Add the broccoli, lemon zest, and remaining 1 tablespoon oil. Stir to combine.
Using the back of a spoon, press down into the vegetables to make 4 shallow divots for the eggs.
Crack one of the eggs into a small bowl or ramekin (without breaking the yolk), and pour into one of the divots. Repeat with remaining 3 eggs.
Season the eggs with the remaining ¼ teaspoon salt.
Cover the skillet and cook for 7 to 8 minutes for runny yolks, or 10 to 11 minutes for firm yolks.
Top with the scallions and serve warm.