Peel the sweet potato and dice into small 1/2-inch cubes to ensure even cooking.
Finely dice the green bell pepper, yellow onion, and celery to create the aromatic base.
Heat the avocado oil in a large non-stick skillet over medium heat.
Add the sweet potatoes to the skillet and cook for 8-10 minutes, stirring occasionally, until they begin to soften and develop a golden exterior.
Stir in the bell pepper, onion, and celery, and continue cooking for 5 minutes until the vegetables are translucent and fragrant.
Gently fold in the lump crab meat, taking care not to break up the large chunks, and sprinkle with Cajun seasoning, sea salt, and black pepper.
Cook for another 3-4 minutes until the crab is heated through and the edges of the hash are slightly crispy.
In a separate small non-stick pan, fry the egg to your preference, ideally sunny-side up or over-easy to allow the yolk to coat the hash.
Transfer the hash to a plate, top with the fried egg, and garnish with freshly sliced green onions.