To make cookie dough, cream butter and powdered Sugar to a smooth paste in a medium bowl.
Add egg yolk, salt and vanilla.
Sift flour; knead into mixture to make a dough.
Press into a ball and wrap in foil or plastic wrap.
Refrigerate 30 minutes.
Preheat oven to 350°F (175°C).
Cut off 1 piece of dough at a time and shape, leaving remaining dough in refrigerator.
On a floured surface, roll each piece of dough pencil thin and 10 inches (25 cm) long.
Twist into a pretzel as illustrated.
Place pretzels on a baking sheet.
Bake 12 to 15 minutes or until golden.
Cool slightly on baking sheet then transfer to a rack with a spatula.
To make frosting, combine egg white, rum, lemon juice and powdered sugar in a medium bowl.
Brush warm pretzels as thickly as possible with rum frosting.