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Preheat oven to 350 degrees. Spray a 9×13 pan with nonstick cooking spray.
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In a medium-size mixing bowl, toss berries with lemon zest and juice, cornstarch, vanilla, and white sugar. Spread them out in the 9×13 pan.
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In a large mixing bowl, stir together flour, powdered sugar, baking powder, and salt. Use a pastry cutter to cut in butter until it resembles a course meal, or pulse the whole thing together in a food processor.
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Pour in half and half and stir to form a thick batter.
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Scoop the batter in large clumps on top of the berries to form a nice cobbler crust.
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Bake in the preheated oven for 1 hour.