Heat the oil in a large (12-inch) skillet, preferably cast iron, over medium heat. Add the sweet potato and 1/2 teaspoon of the salt, stir to coat, and spread in an even layer.
Cover and cook for 8 minutes, stirring once, until the cubes begin to soften.
Uncover, raise the heat to medium-high and add the onion and pepper. Cook for 8–10 minutes, stirring only every couple of minutes, until the vegetables are browned and the sweet potato is tender.
Add the garlic, paprika, cumin and remaining salt and cook for 1 minute. Stir in the greens until wilted.
Make four wells in the hash and crack an egg into each. Season the eggs, cover the pan and cook on medium-low for 4–6 minutes, until the whites are set and the yolks are done to your liking. Sprinkle with green onion and serve.