Preheat the oven to 200°C (400°F) conventional (see note 1 if using a fan-forced convection oven)
Peel, pit, and slice the peaches into wedges (see note 2), then place them into a large bowl. Add in the sugar, cinnamon, salt, lemon juice, cornstarch, and vanilla, then mix well until the peaches are evenly coated.
Transfer the peaches to a 9x13-inch baking dish and spread them out evenly. No need to grease the dish. Bake for 10 minutes to help soften the peaches and release their juices.
While the peaches are baking, prepare the topping. In a large bowl, whisk together the flour, sugar, baking powder, and salt.
Add in the cold, cubed butter and use your fingers or a pastry cutter to rub the butter into the flour mixture until crumbly with some larger bits of butter throughout.
Next add in the cold milk and vanilla, then gently stir until a soft, shaggy dough forms. The mixture shouldn’t come together into one smooth solid mass — it should look loose and rustic (see video for visual reference). Be careful not to overmix.
Once the peaches are out of the oven, place dollops of the topping all over the peaches and gently spread it out slightly with your hands as you go. It doesn’t need to be perfect, and it’s okay if some of the peaches are peeking through.
In a small bowl, combine the sugar and cinnamon for the topping, then sprinkle it evenly over the cobbler.
Return the cobbler to the oven and bake for 30–35 minutes, or until the topping is golden brown and the peach filling is bubbling around the edges.
Let the cobbler cool for at least 20 minutes before serving to allow the filling to thicken slightly. Serve warm with a scoop of vanilla ice cream!