Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the sliced peaches, 1/2 cup of sugar, cinnamon, and lemon juice. Toss until the peaches are well coated.
Pour the peach mixture into a greased 9x13-inch baking dish.
In another bowl, whisk together the flour, remaining 1/2 cup of sugar, baking powder, and salt.
Gradually stir in the milk, melted butter, and vanilla extract 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 for 45-50 minutes, or until the top is golden brown and a toothpick inserted in the center comes out clean.
Let the cobbler cool for about 10 minutes before serving.