1. Place butter and chocolate in a 3-quart glass mixing bowl. Microwave, uncovered, at Cook Cycle 1 (power level 10)for 2 1/2 to 4 minutes,or until melted. Stir in brown sugar, applesauce, eggs, and vanilla. Blend in flour 1/4 cup at a time. Add baking powder and soda. Stir in nuts. Pour batter into a well-greased 8-inch round baking dish.
2. Microwave, uncovered, at Cook Cycle 2 (power level 5) for 15 to 17 minutes. Cover and let stand 5 minutes, then allow to cool, uncovered. Store in a tightly covered container.