Combine brown sugar, 1/3 cup cocoa, and 2 cups hot water in an ungreased 11 x 7–inch glass or ceramic baking dish, stirring until sugar dissolves.
Weigh or lightly spoon baking mix into dry measuring cups; level with a knife. Combine baking mix and next 3 ingredients in a large bowl, stirring with a whisk. Add oil and next 4 ingredients, stirring just until combined.
Spoon batter over brown sugar mixture in dish. Set dish on a jelly-roll pan. Bake at 350° for 55 minutes or until cake springs back when touched lightly in center. Cool 30 minutes. Spoon cake and sauce into serving dishes.