Bring a medium pot of water to a rolling boil. Carefully lower the eggs into the water and boil for 7 minutes to achieve a jammy, soft-boiled yolk.
Prepare an ice bath while the eggs cook. Immediately transfer the eggs to the ice bath for 5 minutes to stop the cooking process, then peel and set aside.
In a large skillet over medium heat, melt the ghee until it coats the bottom of the pan.
Add the minced garlic to the skillet and sauté for 1 minute until it becomes fragrant and lightly golden.
Stir in the Old Bay seasoning, smoked paprika, sea salt, and black pepper, mixing well with the ghee to bloom the spices.
Add the raw shrimp to the skillet in a single layer. Cook for 2 to 3 minutes per side until they are pink, opaque, and slightly curled.
Turn off the heat and stir in the fresh lemon juice, tossing the shrimp to ensure they are well-coated in the garlic butter sauce.
Slice the peeled eggs in half and nestle them into the skillet among the shrimp.
Spoon the remaining sauce from the pan over the eggs and garnish the entire dish with fresh chopped parsley before serving.