Pour the melted butter into the bottom of the baking dish and spread it evenly.
In a large mixing bowl, combine the flour, sugar, baking powder, and salt.
Pour in the milk and vanilla extract, if using, and whisk until the batter is smooth.
Pour the batter over the melted butter. Do not stir.
Arrange the sliced canned peaches evenly over the batter, then pour about half of the reserved peach syrup over the top.
Sprinkle with cinnamon and nutmeg, if using.
Bake at your tested oven temperature until the top is deeply golden brown, the edges are set, and the peach juices are bubbling.
Remove from the oven and let the cobbler rest briefly before serving. Serve warm, preferably with vanilla ice cream.