To slice eggs, lay each egg on its side and sweep the blade cleanly down the center. Wipe the knife after each egg. You may use either regular or reduced-fat mayonnaise in this recipe. If preferred, use a pastry bag fitted with a large plain or star tip to fill the egg halves.
Bring 1 inch water to rolling boil in medium saucepan over high heat. Place eggs in steamer basket. Transfer basket to saucepan. Cover, reduce heat to medium-low, and cook eggs for 13 minutes.
When eggs are almost finished cooking, combine 2 cups ice cubes and 2 cups cold water in medium bowl. Using tongs or spoon, transfer eggs to ice bath; let sit for 15 minutes. Peel before using.
Slice each egg in half lengthwise with paring knife. Transfer yolks to bowl; arrange whites on serving platter. Mash yolks with fork until no large lumps remain. Add mayonnaise and use rubber spatula to smear mixture against side of bowl until thick, smooth paste forms, 1 to 2 minutes. Add minced parsley, lemon juice, mustard, curry powder, and cayenne and mix until fully incorporated.
Transfer yolk mixture to small, heavy-duty plastic bag. Press mixture into 1 corner and twist top of bag. Using scissors, snip ½ inch off filled corner. Squeezing bag, distribute yolk mixture evenly among egg white halves. Garnish each egg half with parsley leaf and serve.