Place the eggs in a saucepan and cover them with water. Bring to a boil over medium-high heat. Once boiling, cover the pan, remove it from the heat, and let it sit for 10-12 minutes. Drain and transfer the eggs to an ice bath to cool. Peel and set aside.
In a large skillet over medium heat, melt the butter. Add the sliced chicken sausage and cook for 5-6 minutes until browned and slightly crispy on the edges.
Add the minced garlic to the skillet and sauté for about a minute until fragrant. Stir in the Cajun seasoning, Old Bay, paprika, black pepper, and salt. Cook the spices in the butter for another minute to release their flavors.
Add the peeled boiled eggs to the skillet and gently stir to coat them in the seasoned butter sauce. Simmer for 2-3 minutes to let the eggs absorb the flavors. If you prefer a thinner sauce, pour in the chicken broth or water and stir to combine.
Taste and adjust seasoning if needed. Let everything simmer together for a few more minutes.
Garnish with chopped fresh parsley if desired and serve warm.
