PreparationFor filling: Preheat oven to 375°F. Combine apples, blackberries, sugar, cornstarch, honey, butter, and lemon juice in a large bowl and toss to evenly distribute. Transfer mixture to a shallow 3-quart baking dish and set aside. For biscuit topping and assembly: Combine polenta, baking powder, salt, 1 1/2 cups flour, and 1/4 cup sugar in a food processor; pulse to blend. Add butter and pulse until pea-size lumps form. Transfer flour mixture to a large bowl and form a well in the center. Add 1 cup cream to well and mix with a spoon or spatula until a shaggy dough forms. Transfer mixture to a lightly floured work surface and knead just until dough comes together, about 3 times. Pat or roll out dough into a 14x4" rectangle about 1/2" thick. Cut dough rectangle in half lengthwise, then cut each strip crosswise into 6 equal pieces to make 12 biscuits. Arrange biscuits over fruit mixture, spacing about 1/2" apart. Brush biscuits lightly with cream and sprinkle evenly with sugar. Bake cobbler until filling is bubbling around edges and biscuits are golden brown, 40-50 minutes. Transfer to a wire rack and let cobbler cool for at least 10 minutes. Serve warm or at room temperature. DO AHEAD: Cobbler can be made 6 hours ahead. Let stand at room temperature.
PreparationFor filling: Preheat oven to 375°F. Combine apples, blackberries, sugar, cornstarch, honey, butter, and lemon juice in a large bowl and toss to evenly distribute. Transfer mixture to a shallow 3-quart baking dish and set aside. For biscuit topping and assembly: Combine polenta, baking powder, salt, 1 1/2 cups flour, and 1/4 cup sugar in a food processor; pulse to blend. Add butter and pulse until pea-size lumps form. Transfer flour mixture to a large bowl and form a well in the center. Add 1 cup cream to well and mix with a spoon or spatula until a shaggy dough forms. Transfer mixture to a lightly floured work surface and knead just until dough comes together, about 3 times. Pat or roll out dough into a 14x4" rectangle about 1/2" thick. Cut dough rectangle in half lengthwise, then cut each strip crosswise into 6 equal pieces to make 12 biscuits. Arrange biscuits over fruit mixture, spacing about 1/2" apart. Brush biscuits lightly with cream and sprinkle evenly with sugar. Bake cobbler until filling is bubbling around edges and biscuits are golden brown, 40-50 minutes. Transfer to a wire rack and let cobbler cool for at least 10 minutes. Serve warm or at room temperature. DO AHEAD: Cobbler can be made 6 hours ahead. Let stand at room temperature.