Gently place the eggs in a single layer at the bottom of a medium pot. Fill with cold water to cover eggs by 1-2 inches. Heat the pot on high and bring the water to a rolling boil. Once it starts boiling, turn off the heat, remove the pan from the burner, cover, and let sit for 6 to 7 minutes for a soft yolk, 8 to 9 minutes if you prefer a more set yolk, or 12 to 14 minutes for hard boiled eggs.
Using a slotted spoon, transfer the eggs to a large bowl of ice water and leave submerged for 2-3 minutes. (This will cool them quickly and prevent further cooking, plus make them easier to peel.)
When the eggs are cool to the touch, gently peel them and set aside while you make the sauce.
Stir in 1 tablespoon brown sugar and a 1/4 teaspoon EACH old bay seasoning, smoked paprika, dried oregano, garlic powder, onion powder, lemon pepper seasoning, coarse salt, and crushed red chili flakes; mix well.
Pour in 1/2 cup low-sodium chicken broth and juice from 1/2 a lemon.
Simmer for 3-4 minutes or until the sauce has reduced slightly.
Remove from heat and pour the sauce over the eggs.