* If using fresh peaches, peel and slice the peaches. In a saucepan, combine the peaches, sugar, cinnamon, nutmeg, lemon juice, and cornstarch. Stir well and cook over medium heat for 5-7 minutes, or until the mixture thickens and the peaches soften.
* If using canned peaches, drain the peaches and mix them with the sugar, cinnamon, nutmeg, and lemon juice in a bowl. You can skip cooking the canned peaches.
Make the batter: In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, and salt. Stir in the melted butter, milk, and vanilla extract until just combined. The batter should be smooth and slightly thick.
Assemble the cobbler: Pour the batter into the prepared baking dish, spreading it evenly. Spoon the peach mixture over the batter, distributing the peaches evenly across the top. As the cobbler bakes, the batter will rise up and around the peaches.
Bake the cobbler: Bake in the preheated oven for 35-40 minutes, or until the top is golden brown and a toothpick inserted into the center of the batter comes out clean.
Cool and serve: Allow the cobbler to cool slightly before serving. Serve warm with a scoop of vanilla ice cream or whipped cream for the perfect finishing touch.