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Place eggs in a saucepan and cover with water. Bring to a boil over high heat, and cook 1 minute. Cover, turn off heat, and let stand for 9 to 10 minutes. Drain and add eggs to a bowl of ice water. Peel eggs and set aside.
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In a large Dutch oven, add sausage and cook over medium-high heat until fat has rendered and sausage is browned. Remove sausage with a slotted spoon to a paper towel-lined plate and set aside.
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Melt butter in the same pot. Add onions and cook, stirring occasionally, until onion has softened, about 3 minutes. Add garlic and cook 1 minute longer. Add Old Bay, 2 1/2 teaspoons Cajun seasoning, 1 teaspoon paprika, oregano, and 1 1/2 teaspoons lemon pepper and stir to combine. Cook until fragrant, about 1 minute. Add stock, water, and potatoes. Add more water if necessary, enough just to cover potatoes. Stir to combine and bring mixture to a boil. Reduce heat slightly to maintain a simmer and cook for 10 minutes. Add corn and continue to cook 10 minutes. Add in reserved eggs and sausage and let simmer gently while wings are prepared.
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Preheat an air fryer to 360 degrees F (182 degrees C).
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Toss wings with oil and remaining Cajun seasoning, paprika, lemon pepper, salt and pepper. Air fry wings cooked through, crispy, and golden brown, about 15 minutes.
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Use a spider or strainer to transfer onions, sausage, potatoes, corn, and eggs from pot to a large, deep serving platter. Add wings to platter and pour over cooking liquid remaining in the pot. Sprinkle with chopped parsley.