Preheat your oven to 375°F (190°C). This ensures that the cobbler bakes evenly.

In a large mixing bowl, combine the sliced peaches, granulated sugar, lemon juice, ground cinnamon, and cornstarch. Toss gently to coat the peaches evenly.

Let the mixture sit for about 10 minutes to allow the peaches to release their juices.

Transfer the peach mixture into a greased 9x13 inch baking dish, spreading it out evenly.

In another mixing bowl, whisk together the flour, baking powder, salt, and sugar until well combined.

Add the cold, cubed butter to the flour mixture. Use a pastry cutter or your fingers to work the butter into the flour until the mixture resembles coarse crumbs. This step creates a flaky texture in the topping.

Pour in the milk and vanilla extract, and stir until just combined. Be careful not to overmix, as this can make the topping tough.

Drop spoonfuls of the batter over the peach filling, covering as much of the surface as possible. It's okay if some peaches are still visible.

Place the baking dish in the preheated oven and bake for 35-40 minutes, or until the topping is golden brown and a toothpick inserted into the topping comes out clean.

Once baked, remove from the oven and let it cool for about 10 minutes before serving. This allows the juices to set.

Scoop the warm peach cobbler into bowls and serve with a generous scoop of vanilla ice cream on top, if desired.