Preparation

Make the filling

Position a rack in the center of the oven, and heat oven to 375°F. Melt the butter in a large skillet over medium heat. Add the sugar and fruit, and continue to cook, stirring often, until sugar is dissolved and juices appear in skillet. Increase heat to medium-high, and cook, stirring occasionally, until fruit begins to break down and the juices begin to thicken, 5 to 6 minutes. Remove from heat.

Make the topping

Combine the flour, cornmeal, granulated sugar, baking powder, baking soda, and salt in a food processor, and pulse to mix. Add the butter, and pulse until the mixture resembles coarse meal, about 30 pulses.

Transfer flour mixture to a medium bowl, add the cream, and mix with a fork. If the dough seems dry after mixing, add more cream, a tablespoon or two at a time, until the dough is soft and moist.

Taste the fruit filling, and add another tablespoon of granulated sugar if you think it needs it. Transfer the fruit to a 9-inch baking dish. Put the dish on a rimmed baking sheet to catch any spills. Spoon the dough over the fruit; it should cover all of it, but no worries if it doesn’t. Sprinkle with turbinado sugar.

Bake until the fruit is bubbling, the topping is golden, and a toothpick inserted in the center comes out clean, 45 to 55 minutes. If the topping begins to brown too quickly, cover lightly with foil. Let cool briefly, and serve warm.