Special equipment: an 11-cup Bundt pan
Preheat the oven to 350 degrees F. Grease an 11-cup Bundt pan.
Melt the butter in a medium saucepan set over medium heat. Continue cooking until the butter turns golden brown, then transfer to a heatproof container and refrigerate until solid, about 1 hour.
In a medium bowl, pour the boiling water and brandy over the figs and soak until softened, about 30 minutes. Coarsely chop 1/2 cup of the figs, and set aside. Place the remaining figs and the soaking liquid in the bowl of a food processor and puree until smooth.
In a stand mixer fitted with the paddle attachment, combine the chilled brown butter with the sugar and beat until combined. Add the eggs one at a time, and mix until combined. Add the fig puree, flour, baking powder, cinnamon and salt, and beat on low speed until smooth. Stir in the chopped figs. Pour the batter into the prepared Bundt pan, then cover tightly with foil and secure with a rubber band.
Place the Bunt pan in a 12-by-17-inch deep roasting pan and set on the bottom rack of the oven. Pour 2 inches of boiling water around Bundt pan, then cover entire roasting pan with foil. Bake until the pudding is firm to the touch and a toothpick inserted in the center comes out clean, about 1 hour 15 minutes.
Cool the pudding for 10 minutes, then invert the Bundt pan over a plate to unmold the pudding. Sprinkle the pudding with confectioners' sugar and cut into slices to serve.