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In a bowl, toss the berries with the sugar and cornstarch and let stand for 10 minutes.
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Preheat the oven to 375°. In a medium bowl, whisk the flour with the sugar, lemon zest, baking powder and salt. In a small bowl, whisk the eggs with the milk and vanilla. Whisk the liquid into the dry ingredients until evenly moistened, then whisk in the melted butter until smooth.
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Spread the filling in a 9-by-13-inch baking dish. Spoon the batter on top, leaving small gaps. Bake in the center of the oven for 1 hour, until the fruit is bubbling and a toothpick inserted into the topping comes out clean. Let cool for 1 hour before serving.