Place six to eight eggs in a large pot and cover them with water, ensuring the water is about an inch above the eggs. Bring the water to a rolling boil over high heat, then lower the heat to maintain a gentle boil for about 10-12 minutes. Once cooked, transfer the eggs to an ice bath for 5 minutes, allowing them to cool and making them easier to peel.

In a medium saucepan, melt four tablespoons of unsalted butter over medium heat until it starts to bubble. Add one small sliced onion to the pan; sauté for about 3-4 minutes until the onion softens and becomes fragrant.

Stir in two tablespoons of minced garlic and one teaspoon of garlic paste, cooking briefly for 1-2 minutes until aromatic.

Sprinkle in one tablespoon of Old Bay seasoning, half a teaspoon of cayenne pepper, half a teaspoon of smoked paprika, one teaspoon of garlic powder, and one teaspoon of onion powder. Stir and cook for an additional minute.

Pour in one cup of vegetable broth and stir well. Increase the heat slightly to bring the mixture to a simmer, then reduce heat and let it simmer for about 5 minutes.

Carefully peel the boiled eggs and place them in a serving bowl. Pour the spicy garlic butter sauce over the eggs, ensuring they are thoroughly coated.

Serve the Cajun Boiled Eggs warm or allow them to cool slightly and enjoy them chilled. Garnish with additional cayenne pepper or fresh parsley.