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Preheat the oven to 425 degrees F.
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In a 2 - 3-quart ovenproof dish, gently fold the blackberries, sugar, ginger, lemon juice, flour, cinnamon, and sea salt together. Add peaches at the last minute.
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Next, make the biscuit topping by combining the flours, 2 tablespoons sugar, baking powder, and sea salt. Grate in the butter and massage into flour with fingertips. Using a silicone spatula, fold in the buttermilk, stirring just until a sticky ball of dough forms.
Using two spoons, top the fruit filling with approximately 9 2-inch dollops of biscuit dough. Sprinkle biscuit tops with remaining tablespoon of sugar.
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Bake 20 - 25 minutes, or until biscuits are a light golden brown and the filling is bubbling vigorously. Cool for 15 minutes; serve with buttermilk whipped cream.
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To make the buttermilk whipped cream, beat cream to very soft peaks in a large bowl (to avoid flying bits of cream). Switch mixer to medium, add sugar, and then gradually add buttermilk, maintaining soft peaks all the while.