Preheat the oven to 200°C (without fan).
Halve the peaches and remove the stone. I leave the skin on the peaches because they give the syrup a lovely colour.
Cut the peaches into thick slices.
Place the peach slices into a baking dish with 1 litre/4 cup capacity. You want enough peaches to completely fill the baking dish in one layer, plus a few more on top. As the peaches bake, they will shrink in size a little.
Sprinkle the sugar and cornflour (US: cornstarch) over the peaches.
Pour over the lemon juice and water.
Use a spoon to toss the peaches together to make sure everything is mixed through roughly.
Place the baking dish into the oven on the top shelf.
Bake the peaches for about 15 minutes, and then use a spoon to gently turn and stir the peaches.
While the peaches are baking, prepare the cobbler topping (see instructions below).
Bake the peaches for another 10-15 minutes, or until the peaches have started to soften, and the liquid underneath has started to thicken into a syrup. You should aim to have enough liquid to come halfway up the peaches. If there is not much liquid in the dish (this can happen if your peaches are not particularly juicy or ripe enough), add a few tablespoons of water to the dish. Generally speaking, the peaches should be sitting in enough liquid to gently cook and soften; if there is not enough liquid, the peaches will not soften and cook down, and nor will there be enough sauce in the dish later.