Open the can of sweetened peaches and pour the syrup into a bowl—set aside 2 tablespoons of this syrup for later. If the peach slices are large, cut them in half. No need to cook them, just drain well.
In a medium bowl, whisk together the instant vanilla pudding mix and milk. Whisk for about 2 minutes until it thickens. Stir in the reserved 2 tablespoons of peach syrup to infuse the pudding with extra fruity flavor.
In a separate bowl, mix together the flour, sugar, baking powder, and salt. Slowly pour in the milk while whisking to avoid lumps. Then stir in the melted butter until smooth. The mixture will be pourable but not runny.
Pour the cobbler batter evenly into a greased 9x13 dish. Carefully spoon the vanilla pudding on top of the batter and spread it evenly with a spatula. Arrange the sliced peaches over the pudding layer, distributing them evenly for a colorful, fruity top.
Cover the dish tightly with plastic wrap or a lid and refrigerate for at least 2 hours. Overnight chilling will yield the best texture. The layers will settle and firm up beautifully.
Just before serving, add a generous dollop of whipped cream and a sprinkle of crushed graham crackers or cinnamon. The contrast in texture elevates every bite.