Preheat the oven to 400ºF (200ºC) and line a baking sheet with parchment paper.
Grease an 8-inch (20 cm) round baking dish with the butter. Add the blueberries to the greased dish and spread them into an even layer. Set aside.
In a large bowl, whisk together the flour, sugar, and salt until well combined. Add the milk and continue to whisk until the flour is absorbed into the milk.
Add the eggs and vanilla to the bowl. Whisk everything together to a smooth batter.
Pour the batter over the blueberries in the prepared baking dish. Place the dish on the parchment lined baking sheet, and place the sheet in the preheated oven.
Bake the blueberry clafoutis for 40 to 45 minutes, or until the edges are puffed and golden, and the middle is set.
Transfer the clafoutis to a wire rack. The top will probably be cracked, and the edges will deflate as it sits — this is typical!
Cool the clafoutis for 15 minutes before serving with a dusting of powdered sugar.