Preheat the oven to 300 degrees. Butter a 9 by 13-inch cake pan and line it with parchment or waxed paper.
In the top of a double boiler set over barely simmering water, melt the chocolate and butter together. Stir well and set aside to cool slightly. Meanwhile, in a mixer fitted with a whisk attachment (or using a hand mixer), whip the egg yolks and 1/2 cup of the granulated sugar until very light yellow and fluffy. In a clean, dry bowl, whip the egg whites until soft peaks form. Add the remaining 1/4 cup sugar and continue whipping just until stiff and glossy, about 30 seconds more. Fold the egg yolks into the hot chocolate mixture until barely blended. Fold in the whites until barely blended. Sprinkle the brandy and polenta evenly over the surface of the batter and fold in. Pour into the prepared pan and bake until the center is firm and a tester inserted into the center comes out clean (a few crumbs are okay), 1 to 1 1/4 hours. Let cool in the pan. Cut into squares, dust with confectioner's sugar, and serve.
Recipe courtesy of Gale Gand, "Butter Sugar Flour Eggs" by Gale Gand, Rick Tramonto, Julia Moskin, Clarkson N. Potter Publishers, 1999