Sift flour into a large bowl.
Make a well in the center of flour; add upflavored sugar, salt, lemon peel, vanilla sugar, egg and rum.
Dot butter over flour; knead to a soft dough.
Press into a ball and wrap in foil or plastic wrap.
Refrigerate 30 minutes.
Preheat oven to 350°F (175°C).
Grease baking sheets.
On a floured surface, roll out cookie dough, a little at a time 1/8 inch (3 mm) thick.
Using a plain cutter and a ring cutter of the same size, cut out equal quantities of rounds and rings.
Place on baking sheets.
Bake 10 to 15 minutes or until golden.
Remove from baking sheet with a spatula; cool slightly on a rack.
Sift powdered sugar generously onto rings.
Warm jam over low heat; spread jam smoothly onto warm rounds.
Place sugared rings on top of rounds.
Adda little more jam to centers of rings.
Cool completely before storing in an airtight container.