Melt the butter in a medium pot or skillet.
Add the minced garlic and cook until fragrant (about 1 minute).
Stir in the remaining spices. Add the broth. Let the mixture simmer on low heat for 5 minutes until the egg boil sauce has slightly thickened.
Remove the sauce from heat. Stir in the lemon juice.
Add the boiled eggs to the egg sauce mixture. Serve.