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Cook the potatoes in boiling salted water for 5 mins, then drain and let steam-dry. Heat half the butter and oil in the pan and fry the potatoes for about 10-15 mins until golden. Add the chopped chilli, garlic, Cajun seasoning, sweetcorn and black beans, and heat through for about 5 mins, then season.
Keep warm in a low oven while you fry the eggs in the rest of the butter and oil until cooked to your liking. Divide the potatoes between 2 bowls and top with an egg, some chopped avocado and the sliced chilli. Serve with lime wedges, soured cream and warm tortillas, if you like.