Place eggs in a single layer in a saucepan. Add water to cover by 1 inch. Bring to a rolling boil over high. Cover, remove from heat, and let stand 10 minutes. Drain.

Submerge eggs in ice-cold water; let stand 10 minutes. Tap each egg firmly on the counter until cracks form all over the shell. Peel under cold running water.

Slice eggs in half lengthwise; remove yolks, keeping egg white halves intact.

Using fine holes of a grater, grate yolks into a bowl. Stir in mayonnaise, okra brine, parsley, mustard, salt, and pepper. Spoon or pipe filling into egg whites. Top each deviled egg with 1 slice of pickled okra.