Preheat oven to 350 degrees F. Lightly butter a 9-inch-square baking pan.
To make the biscuit topping: Combine the flour, baking powder, salt and nutmeg in a mixing bowl or your food processor.
Cut the cold butter into pats, and then cut them into the flour using your fingers, a pastry blender or the metal blade of your food processor, until the largest pieces of butter are the size of peas.
Mix in the 2 tablespoons brown sugar quickly.
Beat the egg with the milk and add to the flour mixture all at once. Mix gently, just until combined; the dough will be a bit wet and sticky. Let it rest while you make the filling.
To make the fruit filling: Combine the peaches and blueberries in a large bowl.
In a small bowl, mix the ½ cup brown sugar with the cornstarch, nutmeg and salt.
Add the sugar mixture to the fruit and stir gently to combine.
Turn the fruit into the buttered baking pan and sprinkle with the lemon juice. Set aside while you finish the biscuits.
Generously dust your work surface with flour and turn the dough out onto it.
Flour your hands and pat the dough into a circle about ¾ to 1 inch thick. During this process, reflour your hands liberally whenever the dough starts to stick to them.
Using a well-floured biscuit cutter, cut the biscuits and "cobble" them together over the peaches and blueberries.
Try to cover the entire surface of the fruit.
Sprinkle the top with sparkling sugar, if you like.
Place the pan in the oven. Bake the cobbler until the topping is browned and the fruit is bubbling and thickened, 40 to 45 minutes.
Remove from the oven and cool for 10 minutes before serving.
Serve warm with whipped cream or ice cream.