Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with butter or non-stick spray.
In a large bowl, combine the sliced peaches, 1/2 cup of sugar, lemon juice, and cinnamon. Toss until the peaches are well coated. Pour the peach mixture into the prepared baking dish.
In another bowl, whisk together the flour, baking powder, salt, and remaining 1/2 cup of sugar. Gradually add the milk, melted butter, and vanilla extract, stirring until just combined. The batter will be thick.
Pour the batter over the peaches in the baking dish. Do not stir; the batter will rise during baking.
Bake in the preheated oven for 40-45 minutes, or until the top is golden brown and a toothpick inserted in the center comes out clean.
Allow the cobbler to cool for about 15 minutes before serving. This will help the gooey filling set up a bit more.