Prep an ice bath: Fill a medium bowl with cold water and plenty of ice; set aside.

Boil the eggs (jammy yolks): Bring a saucepan of water to a rolling boil. Lower in eggs gently; boil 7 minutes for runny-jammy or 7½ minutes for more set yolks (start the timer when the last egg goes in).

Shock & cool: Transfer eggs to the ice bath for ~2 minutes until cool enough to handle.

Peel: Under a slow stream of cool water, crack and peel each egg; pat dry and set aside.

Garlic-butter base: In a large skillet over low heat, melt butter. Add minced garlic; stir 1 minute until fragrant (do not brown).

Bloom spices: Stir in Old Bay, brown sugar, onion powder, lemon pepper, paprika, and chili flakes. Cook 1 minute to bloom spices and dissolve sugar.

Simmer: Add broth; raise heat to medium-high. Simmer ~6 minutes, stirring, until slightly reduced and glossy (it should coat a spoon).

Brighten & season: Stir in lemon juice. Splash in water if you want a looser sauce. Taste; add kosher salt only if needed.

Sauce & serve: Place peeled eggs in a serving bowl; pour hot sauce over. Garnish with parsley. Serve as-is—or with crusty ciabatta or steamed jasmine rice.