In a medium heavy saucepan, combine sugar and cornstarch. Beat milk into egg; gradually stir in sugar mixture. Cook and stir over medium heat until mixture boils and thickens. Remove from heat; stir in vanilla. Cover surface with plastic wrap; chill. Just before serving, arrange peaches in a 9-inch quiche dish or pie plate. Stir chilled custard until smooth and spoon over fruit. Sprinkle brown sugar evenly over top. Broil 4 - 5 inches from heat source, for 2 - 3 minutes, or until sugar melts and bubbles. Serve immediately.