Sauté mushrooms and onion in 2 tablespoons butter in a large skillet until tender. Add broth, 1 1/2 cups brown sauce, olives, lemon juice, and pepper, stirring well. Cook over medium heat 5 minutes, stirring constantly. Remove from heat, and set aside.
Wash livers; pat dry, and sprinkle with salt. Sauté livers in remaining butter in a large skillet 5 minutes or until livers are lightly browned. Warm cognac; ignite and pour over livers in skillet. Transfer livers to serving platter with hot cooked rice, reserving pan drippings in skillet. Add reserved mushroom mixture to pan drippings, stirring well; heat thoroughly. Spoon mixture over livers; serve immediately.