Put oven rack in middle position and preheat oven to 400°F. Butter an 8-inch square glass or ceramic baking dish.
Stir together water, cornstarch, and 1/3 cup sugar in a small saucepan, then stir in rhubarb. Bring to a simmer, stirring constantly, then simmer, stirring occasionally, 3 minutes.
Remove from heat and stir in strawberries.
Whisk together flour, baking powder, salt, and remaining 1/2 cup sugar in a bowl.
Whisk together egg, milk, butter, and vanilla in a large bowl, then whisk in flour mixture until just combined.
Reserve 1/2 cup fruit mixture, then add remainder to baking dish and pour batter over it, spreading evenly.
Drizzle reserved 1/2 cup fruit mixture over batter.
Bake until a wooden pick inserted into center of cake portion comes out clean, 25 to 30 minutes. Cool in pan on a rack 5 minutes before serving.
