Heat a large non-stick frying pan over medium heat. Add 1 tablespoon of oil, onion and chorizo. Cook until onion is browned and chorizo is starting to crisp, about 5 minutes. Using a slotted spoon, remove and set aside.
Return pan to the heat, add remaining oil, potatoes, sweet potatoes and ¼ teaspoon salt. Cook, stirring occasionally until potatoes are tender and have browned, about 10-12 minutes.
Add tomato, kale and remaining ¼ teaspoon salt. Cook another 3 minutes until kale is wilted. Return onion and chorizo to pan, stir to combine and create 4 wells in the hash. Crack eggs into wells, reduce heat to low, cover and cook until eggs are set, about 6-8 minutes.
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