Preheat oven to 350 degrees F.: Warmth in the oven gives you a predictable bake environment and allows the topping to set as the filling begins to bubble. You should feel a steady heat from the oven when you open it, and the rack positioned in the center helps even browning. A common mistake is not preheating long enough, which can make the topping take longer to brown while the filling overcooks, so wait until the oven reaches temperature before sliding the dish in.
Prepare the Filling: Combine the sliced peaches, lemon juice, sugar, cinnamon, nutmeg, salt and tapioca in a large bowl; set aside for 10-15 minutes.: The moment you mix the peaches with the sugar and spices, a fragrant syrup will begin to form; the air will fill with the scent of warm cinnamon and stone fruit. This resting period lets the sugar draw out juices, and the ground instant tapioca begins to absorb moisture, preventing a runny final filling. A useful cue is seeing glossy liquid pool around the slices, and the fruit should remain intact not mushy. Avoid stirring aggressively or chopping the slices too small, or the filling can turn pasty rather than saucy.
Make the Cobbler Topping: Whisk together the flours, baking powder, baking soda, sugar and salt in another large bowl. Toss the butter pieces with your fingers, and work them into the flour mixture until it is the texture of coarse meal, with little pea-size pieces. Pour the buttermilk on top and, using a fork, mix until just combined.: As you work the cold butter into the dry mix, aim for a sandy texture with visible pea sized bits of fat; these pockets are what create a tender, layered topping. When you pour the buttermilk , the mixture should come together into a slightly sticky dough but not be overmixed. You will notice a fresh, milky tang and the dough holding together when pressed. Overworking will warm the butter and yield a tougher crust, so handle it briefly and with cool hands.
Pour the peaches into a 9×13-inch (or other 3-quart) baking dish. Drop the cobbler topping dough by the spoonful all over the peach filling.: Spoonfuls of dough scattered over the glossy peach layer create a rustic look that bakes into pockets of golden topping. The visual cue to aim for is both covered and exposed fruit, so steam can escape and the filling can bubble. You should hear a soft plop as dollops land on the fruit, and the contrast between the shiny filling and drier dough is clear. Try not to press the dough into the filling; leaving it mounded helps create texture as it bakes.
Bake until the fruit is bubbling and the topping is golden brown, 50 to 60 minutes. Serve warm or at room temperature with vanilla ice cream or whipped cream.: During baking you will see the filling bubble through gaps, and the topping will turn a warm golden brown with edges slightly crisp. The aroma will deepen, carrying notes of caramelized sugar and spice; listen for an occasional gentle bubbling sound as the fruit simmers. If the top browns too quickly before the filling bubbles, tent with foil to prevent burning while the center finishes. A good indicator of doneness is vigorous bubbling in the center and a uniformly golden topping.