Heat the oven to 180°C (356F).
Put the peaches, water, vanilla, and ½ cup of sugar in a saucepan over medium heat. Mix and cook for 6-8 minutes. When the sugar is dissolved and the peaches are soft, turn off the heat and let the mixture cool a little.
In a bowl, add the flour, baking powder, salt, oat flakes, milk, and the rest of the sugar. Mix until you get a creamy consistency.
In a baking pan, add the melted butter, then arrange the peaches without the accumulated liquid on top of the butter. Pour the soft dough over the entire surface to cover the peaches.
Put in the oven and cook for 35-40 minutes, until the cobbler turns golden.
Serve warm, with vanilla ice cream or whipped cream.