Melt butter in a 10-in. cast-iron or oven proof skillet. Sprinkle brown sugar over butter. Arrange plum halves, cut side down, in a single layer over sugar; set aside.
In a large bowl, beat eggs until thick and lemon-colored; gradually beat in sugar. Combine the flour, baking powder and salt; add to egg mixture and mix well. Blend water and lemon extract; beat into batter. Pour over plums.
Bake at 350° for 40-45 minutes or until a toothpick inserted near the center comes out clean. Immediately invert onto a serving plate. Serve warm with whipped cream if desired. Yield: 8-10 servings.