Preheat your oven to 375°F (190°C), and butter your baking dish to prevent sticking.
Spread the fresh blackberries evenly across the bottom of the prepared dish, creating a colorful berry layer.
In a mixing bowl, whisk together the eggs and sugar until the mixture is smooth, slightly pale, and fragrant.
Add the vanilla extract and melted butter to the egg mixture, whisking until well combined and glossy.
Gradually whisk in the sifted flour, blending until the batter is smooth, slightly runny, and free of lumps.
Pour the batter evenly over the blackberries, allowing it to gently cover the fruit and fill the dish about three-quarters full.
Place the dish in the oven and bake for about 35 minutes, until the clafoutis is puffed, golden around the edges, and a inserted toothpick comes out clean.
Remove from the oven and let it rest for a few minutes; the custard will settle and become beautifully tender.
Slice into portions, exposing the soft, custardy interior with juicy blackberries on top, and serve warm or at room temperature.