1Preheat oven to 400 degrees F (200 degrees C). Grease a 9x13-inch baking dish.
2Sift flour, sugar, baking powder, and salt together in a bowl. Cut 1/4 butter into flour mixture with two knives or a pastry blender until mixture resembles coarse crumbs.
3Whisk milk and egg together in a bowl; stir into flour mixture until just moistened.
4Spread blueberries in the bottom of the prepared baking dish. Sprinkle tapioca powder over blueberries; drizzle lemon juice over the top. Dot remaining butter pieces over blueberries. Drop batter in mounds over the blueberry mixture.
5Bake in the preheated oven until cobbler is golden and bubbling, about 30 minutes.