Preheat your oven to 350°F (175°C).
In a mixing bowl, combine the sliced peaches, 1/2 cup of sugar, and lemon juice. Toss to coat the peaches evenly and set aside to marinate for about 10 minutes.
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. Do not overmix; a few lumps are okay.
Pour the batter into a greased 9x13-inch baking dish.
Spoon the marinated peaches and their juices evenly over the batter.
Sprinkle the ground cinnamon on top.
Bake in the preheated oven for 40-45 minutes, or until the cobbler is golden brown and a toothpick inserted into the center comes out clean.
Allow to cool for about 10 minutes before serving.