Prepare an ice bath: Fill a medium bowl with cold water and ice cubes to cool the eggs after boiling.

Boil the eggs: In a medium saucepan, bring water to a rolling boil, add the eggs and boil for 7 minutes for jammy yolks, or 10-12 minutes for hard-boiled eggs.

Cool the eggs: Transfer the cooked eggs to the ice bath using a slotted spoon and cool for about 2 minutes.

Peel the eggs: Peel the eggs under running water to prevent shell fragments from sticking.

Melt the butter: In a large skillet over low heat, melt the unsalted butter.

Sauté the garlic: Add the minced garlic to the skillet and cook for 1 minute until fragrant.

Combine seasonings: Stir in the Old Bay, brown sugar, onion powder, lemon pepper, paprika, and red chili flakes. Cook for another minute.

Add broth: Pour in the broth and increase the heat to medium-high, simmer for around 6 minutes until thickened.

Finish the sauce: Mix in lemon juice and adjust seasoning with kosher salt if desired.

Serve and garnish: Place the peeled eggs in a bowl, pour the sauce over them, and sprinkle with chopped parsley.