Make bars: Preheat oven to 350 degrees. Butter a 10-by-15-inch rimmed baking sheet. Line bottom with parchment paper, and butter parchment; set aside. Whisk together flour, baking powder, baking soda, ground ginger, cinnamon, nutmeg, salt, pepper, and cloves in a medium bowl; set aside.
Put butter in the bowl of an electric mixer fitted with the paddle attachment. Beat on medium speed until smooth. Add brown sugars; mix until pale and fluffy, about 2 minutes. Mix in egg and yolk, and molasses. Reduce speed to low; gradually mix in flour mixture. Mix in 1/2 cup candied ginger and the raisins.
Spread dough evenly onto prepared baking sheet. Bake, rotating sheet halfway through, until firm, 18 to 22 minutes. Let cool completely in baking sheet on a wire rack.
Make icing: Put brown sugar, milk, and butter in a medium saucepan over medium heat. Cook, stirring constantly, until butter has melted and sugar has dissolved. Remove from heat; whisk in vanilla and confectioners sugar. If icing is too thick to drizzle, stir in more milk, a teaspoon at a time. If icing is too thin, stir in more confectioners sugar, a teaspoon at a time. Let cool slightly.
Drizzle bars with icing; sprinkle with remaining 1/2 cup candied ginger. Let stand until icing has set, about 15 minutes. Cut into 2-inch squares. Bars can be stored in single layers in airtight containers at room temperature up to 5 days.