Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the sliced peaches, raspberries, 1/2 cup of sugar, lemon juice, and vanilla extract. Toss gently to coat the fruit and set aside to marinate for about 10 minutes.
In another bowl, whisk together the flour, baking powder, salt, and remaining 1/2 cup of sugar.
Gradually stir in the milk and melted butter until just combined. Do not overmix; a few lumps are okay.
Pour the batter into a greased 9x13-inch baking dish.
Spoon the marinated fruit mixture evenly over the batter, making sure to distribute the peaches and raspberries evenly.
Sprinkle the cinnamon over the top.
Bake in the preheated oven for 40-45 minutes, or until the cobbler is golden brown and a toothpick inserted in the center comes out clean.
Let it cool for about 10 minutes before serving.