Preheat the oven to 375°F (190°C). To make the biscuits, in a large bowl, stir together the flour, baking powder, and salt. Scatter the butter pieces on top and pinch into the flour mixture with your fingertips. Continue to pinch and toss until the mixture has the consistency of a uniform coarse, sandy meal. Add the milk and stir with a wooden spoon just until combined and a moist dough forms. Turn the dough out onto a lightly floured work surface and divide into 12 equal pieces.
To make the filling, in another large bowl, whisk together the sugar, cornstarch, salt, and lemon zest and juice. Add all of the berries and toss gently until well combined (hands work best). Pour the filling into a 9-by-12-inch (23-by-30-cm) baking dish and spread in an even layer. Arrange the biscuits on top of the filling, spacing them evenly. Brush each biscuit lightly with the cream and sprinkle with sugar.
Bake until the biscuits are golden brown and the filling is bubbling, 45–50 minutes. Remove from the oven and let cool for about 15 minutes. Serve warm with vanilla ice cream or whipped cream.