Preheat the oven to 350°F (175°C).
Place a 9x13-inch baking dish on the counter.
Add the butter to the baking dish and put it in the warming oven to melt. Keep an eye on it so it doesn’t brown. When melted, remove the dish and set aside.
In a medium bowl, combine the peaches, sugar, lemon juice, vanilla, cinnamon, cornstarch, and a pinch of salt.
Stir gently to coat. If using canned peaches, drain them well and reduce the added sugar slightly.
In a separate bowl, whisk together the flour, sugar, baking powder, and salt. Add the milk and vanilla, and whisk until smooth.
The batter should be pourable but not thin.
Pour the batter over the melted butter in the baking dish. Do not stir. The butter will rise around the batter and help create a crisp, golden edge.
Spoon the peach mixture evenly over the batter. Do not mix. The batter will rise up around the peaches as it bakes.
Bake for 40–50 minutes, until the top is golden brown and a toothpick inserted into the batter portion comes out clean. The filling should be bubbling around the edges.
Let the cobbler rest for at least 10–15 minutes. This helps the juices thicken slightly and makes scooping easier.
Serve warm with a scoop of vanilla ice cream or a dollop of whipped cream.
Enjoy that cozy hug-in-a-bowl feeling.