Preheat the oven to 375 degrees F (190 degrees C). Whisk flour, 1/2 cup sugar, baking powder, and salt in a mixing bowl; set aside. Grease a 9x13-inch baking dish.

Beat egg, butter, and milk in a bowl until smooth. Stir in flour mixture until moistened, then spread into the prepared baking dish. Stir together rhubarb, 2 cups sugar, and water; pour into the prepared baking dish.

Bake in the preheated oven until dough has set and rhubarb is bubbling, about 40 minutes.