Cream butter in a large mixing bowl; gradually add sugar, beating 5 minutes at medium speed of an electric mixer. Sift together flour, cocoa, and salt; add to creamed mixture alternately with eggs, beginning and ending with flour mixture. Beat well after each addition. Add vanilla and 1/2 cup half-and-half, beating well.
Spoon mixture into a well greased and floured 1 1/2-quart pudding mold, and cover tightly with lid.
Place mold on rack in a large stockpot; add boiling water to a level even with bottom of rack. Bring to a boil. Cover; reduce heat to low; and simmer 2 hours, adding water as needed. Remove mold from water; let cool 2 minutes. Unmold onto a serving platter. Slice and serve with Brandy Sauce.