Slice eggs in half, lengthwise, and remove yolks. Press yolks through a fine sieve into a bowl. Add ¼ cup Cheez-It crumbs, ¼ cup mayonnaise, and mustard, parsley, salt, and pepper. Blend well.
Refill centers of egg whites with yolk mixture. Press two filled halves together. Dip one end of stuff eggs in remaining mayonnaise, then into the remaining cracker crumbs.