Preheat oven to 350°. Put figs in a small bowl and pour in boiling water to cover.
Spray pans with cooking spray. In a bowl, using a mixer on medium speed, beat brown sugar with 1/2 cup butter until fluffy and pale, then add molasses, 1 tsp. vanilla, egg, egg yolk, spices, and salt and beat well.
Whisk flour, baking powder, and baking soda in a bowl. With mixer on low speed, gradually add flour mixture to wet mixture and beat until smooth; then beat in 3/4 cup boiling water. Drain figs and stir into batter.
Divide batter among pans and bake until a toothpick inserted in centers comes out clean, 20 minutes. Cool cakes 10 minutes, then invert onto a rack, using a small spatula or knife if necessary to loosen them.
Beat 6 tbsp. butter in a bowl until creamy, with mixer on medium speed. Add 1 1/2 cups powdered sugar, 3/4 tsp. vanilla, and milk and beat until smooth. You should be able to stand a spoon in it; if not, beat in a little more powdered sugar to thicken.
Slice thin strips of ginger from discs using a vegetable peeler. Dip peeler in hot water and dry off between slices to keep ginger from sticking. You will need 70 to 100 strips to top cakes.
Spread frosting onto cakes and arrange ginger strips in a bow pattern on tops of cakes. Sprinkle with sugar to finish.
*Find Australian crystallized ginger in the baking aisle.