Preheat the oven to 425 degrees F.
For the blueberries: Place the blueberries in a large bowl and sprinkle in the sugar and lemon juice. Add the flour and stir to combine.
For the dough: In a separate bowl, combine the flour, sugar, baking powder and salt. Stir it around, then add the cold butter and use a pastry blender to cut the butter into the dry ingredients.
Whisk together the milk and egg in a small bowl, then drizzle it into the flour-butter mixture and stir until the dough just comes together. It should be lumpy and clumpy!
Pour the blueberries into a 9-by-13-inch baking dish and dot them with the butter, then tear off pinches of the dough and dot them all over the top. Sprinkle the top with extra sugar.
Cover lightly with foil and bake for 20 minutes, then remove the foil and bake until lightly browned, about 25 more minutes. Serve warm or at room temperature with a big scoop of vanilla ice cream.