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Preheat an oven to 325F.
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Peel, core and thinly slice the apples.
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In a medium-sized saucepan over medium-low heat, cook apples, sugar, and lemon juice, stirring occasionally, until apples are soft. Remove from heat. Stir in blackberries and cornstarch.
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Spread the fruit mixture in a baking dish that is 12 to 14 inches in diameter.
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In a bowl, stir together the flour, brown sugar, oats, coconut, almonds, cinnamon and ginger. Drizzle with the melted butter and toss with a fork to combine. Sprinkle this mixture evenly over the fruit. Bake until golden and crisp, 45 to 50 minutes. Serve warm.