Place cake pieces in a food processor; process until coarsely crumbled. Place crumbs in to a large bowl; set aside. Place cereal, almonds, and crystallized ginger in food processor; pulse 1 minute or until finely chopped (mixture will resemble sand). Stir into cake crumbs.
Stir butter, ground ginger, and lemon extract into crumb mixture until moistened. Shape rounded tablespoonfuls of dough into crescent shapes; place on greased baking sheets. Bake at 350° for 15 to 17 minutes or until lightly browned. Cool on baking sheets.
Microwave white chocolate morsels and milk at MEDIUM HIGH (70% power) 1 minute or until morsels melt; stir until smooth. Stir in lemon rind. Dip 1 end of each biscotti into chocolate mixture; place on wire racks until chocolate is firm.
*For testing purposes only, we used Quaker Oat Cinnamon Life cereal.