Preheat oven to 350°F. Place butter in a 9x13-inch baking dish and melt it in the oven.
Prep peaches: Toss sliced peaches with sugar, cinnamon, and lemon juice. Let sit 10 minutes.
Make the batter: Whisk flour, sugar, baking powder, salt, milk, and vanilla until smooth.
Assemble cobbler: Pour batter into dish over melted butter (do not stir). Spoon peaches and juices over batter (again, don’t stir).
Bake for 40–45 minutes until the top is golden brown and edges are crisp.
Cool slightly and serve warm, optionally with ice cream or whipped cream.