Beat shortening at medium speed with an electric mixer until fluffy; add sugars, beating well. Add egg, beating until blended.
Combine flour and next 4 ingredients in a separate bowl; gradually add to sugar mixture, beating after each addition.
Stir cereal, vanilla, and white chocolate into mixture.
Drop by tablespoonfuls onto ungreased baking sheets; flatten with fingertips. Bake at 350° for 10 minutes or until lightly golden. Cool slightly on cookie sheets; remove to wire racks to cool. Store in tins.
Place marshmallows on a long stick or skewer; toast over low heat (below 300°), 3 to 5 minutes or until golden. Place 1 marshmallow on a cookie, and top with a second cookie.
Note: In testing, we used Ghirardelli white chocolate bars.