Preheat oven to 350 degrees F.
Place blueberries in the bottom of a small rectangular glass pan (about 8 by 10 inches).
In a medium bowl, crack eggs and whisk lightly. Add sugar and continue whisking until mixture thickens and is pale yellow. Add milk and vanilla; whisk to combine. Add flour and whisk to combine. Add a pinch of fine salt and whisk to incorporate. Pour mixture over berries.
Bake on the center rack of the oven until the clafouti has puffed and the center bounces back when lightly pressed, about 45 minutes, rotating once.
Remove from oven and let cool slightly before cutting. Slice into 8 equal pieces and gently remove from pan with a spatula or cake server. Dust with powdered sugar and serve immediately.