Mix cornstarch and brown sugar in a round glass cake dish (must be microwave-safe). Add water; stir. Stir peaches in gently. Microwave on High (100%) for 6 to 8 minutes, stirring once or twice, or until mixture boils and has thickened. After mixture thickens, stir in butter and lemon juice. Meanwhile, prepare dumpling batter.
Soften butter in a mixing bowl for about 10 seconds over a bowl of warm water. Beat in egg. Add flour, sugar, baking powder and salt. Beat with a wooden spoon just until batter is smooth. Drop batter by spoonfuls in a circle over hot peach mixture (about 6 evenly spaced mounds). Sprinkle a mixture of sugar and cinnamon over batter. Microwave on High (100%) 10 minutes. During the last 2 minutes of cooking, spoon hot peach syrup over dumplings. Serve warm with cream or ice cream.