Preheat the oven to 375 degrees F. Put the berries in the bottom of a 10-inch stainless steel skillet. Use a fork to beat the egg and 1/4 cup water in a small bowl until combined. Put the flour and sugar in the bowl of a food processor and pulse until the mixture is uniform. Drop in the butter cubes, toss with a fork to coat in the flour mixture and pulse until the mixture is crumbly and moist, about 8 long pulses. Add half of the egg mixture and process about 15 seconds. Add the rest and process another 15 seconds.
Dollop the batter over the berries. Spread the batter with the back of a spoon--some berries will poke through, which is fine. Bake until the berries are bubbling and a wooden skewer inserted into the center of the cake comes out with a few crumbs attached, about 30 minutes. Cool slightly and serve.
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