Preheat the oven to 350 degrees Fahrenheit. Grease a 9x13-inch baking dish.
Add the peaches, strawberries, granulated sugar, cornstarch, lemon juice, vanilla extract, and cinnamon to a large mixing bowl. Stir gently until the fruit is evenly coated.
Spread the fruit filling evenly into the prepared baking dish.
In a separate mixing bowl, whisk together the all-purpose flour, granulated sugar, baking powder, and salt.
Add the milk and stir until just combined.
Stir in the melted butter until the batter is smooth.
Pour the cobbler batter evenly over the fruit filling. Do not stir.
Bake for 40 to 45 minutes, or until the topping is golden brown and the fruit filling is bubbly around the edges.
Let the cobbler cool slightly before serving. Serve warm on its own or with whipped cream or vanilla ice cream.