Preheat the oven to 350°F (180°C).
Prepare the filling: Slice the peaches and hull and halve the strawberries. Place the sliced fruit in a 9-inch pie dish (or combine it in a large bowl and transfer it to the pie dish). Add the sugar, lemon juice, and cornstarch. Toss until evenly coated. Set aside.
Make the topping: Whisk together the flour, sugar, baking powder, salt, and baking soda in a medium bowl. Set aside.
In a separate bowl or measuring cup, whisk together the heavy cream and buttermilk. Pour the wet ingredients into the dry ingredients, stirring with a fork just until a shaggy dough forms and no pockets of dry flour remain.
Drop heaping tablespoons of batter over the fruit, leaving a little space between each mound. Brush the tops with heavy cream and sprinkle generously with demerara or granulated sugar.
Bake for 45-55 minutes, or until the topping is golden brown and the filling is bubbling around the edges and between the biscuits.
Let cool for at least 15 minutes. Serve with ice cream or a dollop of whipped cream.