Peel the hard-boiled eggs and slice them in half lengthwise. Carefully remove the yolks and place them into a small mixing bowl. Arrange the egg whites on a serving plate.
Mash the yolks with a fork until very smooth and crumb-free.
Add mayonnaise, gin or vodka (if using), olive brine, garlic powder, salt, and black pepper. Mix until creamy and fully combined.
Stir in the finely chopped olives. Taste the filling and adjust seasoning if needed. Be cautious with additional salt because the olives and brine are naturally salty.
Lightly dip the cut edges of the egg whites into paprika to create a decorative rim.
Spoon or pipe the yolk mixture back into the egg whites.
Garnish each deviled egg half with a whole olive and a small parsley leaf. Sprinkle lightly with paprika if desired.
Serve chilled.