1. Place butter and chocolate in a 3-quart glass mixing bowl. Microwave, uncovered, at Time Cook for 2 to 3 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 Time Cook for 10 to 12 minutes, rotating the dish 1/2 turn after 5 minutes' baking time. Cover and let stand 5 minutes, then allow to cool, uncovered. Store in a tightly covered container.