In a food processor or bowl, whirl or stir flour, sugar, ginger, pepper, baking soda, cocoa powder, cinnamon, allspice, and salt to blend. Add butter; pulse or cut in with a pastry blender until mixture resembles coarse meal.
In a small bowl, mix vanilla, lemon peel, and 1 tablespoon water. Add to food processor or bowl; whirl or stir until dough forms a ball.
Divide dough in half. Roll out each portion between sheets of waxed paper or cooking parchment to about 1/4 inch thick. Stack and chill rolled dough until firm, about 45 minutes (or freeze about 25 minutes).
Cut out cookies with a floured 1 1/2-inch round cutter. Place 1/2 inch apart on buttered or cooking parchment-lined 12- by 15-inch baking sheets.
Bake cookies in a 325° oven until pale brown, about 15 minutes. Transfer to racks to cool completely.
Place white chocolate and shortening in a heatproof bowl set over a pan of barely simmering water (bottom of bowl should not touch water). Remove from heat and stir occasionally until chocolate is melted and mixture is smooth.
Dip each cookie halfway into white chocolate mixture, then place on a baking sheet lined with waxed paper. Drizzle undipped half of cookie with more white chocolate mixture, if desired. Chill just until glaze is set, about 15 minutes.
Nutritional analysis is per cookie.