Make the dough: Combine the flour, sugar, baking powder, baking soda and salt in a large bowl. Cut in the butter using your fingers, two knives or a pastry cutter until the mixture resembles coarse meal. Slowly add the buttermilk and cream and gently mix, using your fingers or a fork, until the mixture just comes together. (Alternatively, combine the flour, sugar, baking powder, baking soda, salt and butter in a food processor and pulse a few times. Add the buttermilk and heavy cream and pulse until the dough just comes together.)
Transfer the dough to a lightly floured surface and sprinkle a bit more flour on top. Lightly flatten the dough using a rolling pin or your hands, fold it over and flatten again. Fold it over once more, then wrap in plastic wrap and refrigerate until chilled, at least 30 minutes and up to 2 days.
Make the filling: Combine the fruit and sugar in a large bowl and let sit at room temperature until the juices begin to release, about 30 minutes. Transfer the mixture to a saucepan and bring to a boil over high heat. Add the cornstarch slurry, bring to a boil and cook until the mixture thickens, about 1 minute. Remove from the heat and stir in the citrus zest and juice and salt.
Assemble the crostata: Preheat the oven to 375˚. Line a baking sheet with parchment paper or aluminum foil. On a floured surface, roll the dough into a 12-inch round, 1/4 inch thick. Transfer the dough round to the prepared baking sheet. Fill the center with the fruit filling, leaving a 2-inch border. Gently fold the border over the fruit, leaving the center exposed, and pleat the border to make a circle. Sprinkle sugar evenly over the dough.
Bake until the crust is golden brown and the fruit is bubbling, about 30 minutes. Let cool for 10 minutes before slicing. Serve warm or at room temperature.
If you're short on time, use jam in place of cooked fruit: Mix 1 cup prepared jam with 2 teaspoons fresh lemon juice.