Preheat the oven to 375°F. Butter a deep-dish 9-inch pie pan. Pile in the peaches, plums, nectarines, and/or berries and sprinkle on the lemon juice, ¼ cup sugar and the cornstarch or tapioca flour. Toss to combine.
Make the biscuits: In a small bowl, mix together the flour, sugar, baking powder, baking soda, and salt. Add the butter and cut it in with a pastry cutter or two knives, or rub it in with your fingers, until the mixture has a granola like texture. In a another small bowl mix together the sour cream and heavy cream, and add that to the flour mixture. Use a fork to mix just until the dough comes together, and use your hand to gently knead it a couple of times in the bowl.
Lightly flour a clean surface and gently pat the dough out to a ½ inch thick disk. Cut circles with a 2-inch biscuit or cookie cutter (or a glass). Pat together the scraps and cut out another circle or two. You can also just cut the dough into strips or squares. Place the pieces of dough over the top of the peaches, making sure that some fruit is visible between the pieces. Bake for about 45 minutes, until the fruit is bubbling and the biscuits are golden brown.
Cool on a wire rack for about 20 minutes, then serve warm with ice cream, whipped cream, or whatever creaminess moves you.