Preheat oven to 400 degrees F (200 degrees C), and line a 9×13 inch baking pan with parchment paper.
Beat 3/4 cup sugar with the butter until the mixture is smooth and creamy, and beat in the egg. Add the baking powder, and stir in the flour, 1/2 cup at a time, alternating with a few tablespoons of the milk, until all the flour and milk have been incorporated. The dough will be sticky, like sugar cookie dough. Spread the dough into the prepared baking dish, creating a raised edge of dough around the dish.
Place the blueberries in a bowl with 1/2 cup of sugar, and mash the berries with a potato masher. Spread the blueberry mixture on top of the crust in an even layer.
Bake in the preheated oven until the crust has browned slightly and the filling is thickened and bubbling, 15 to 25 minutes.