Preheat your oven to 375°F and lightly grease a 9×13-inch baking dish.
Drain the peaches and reserve 1/2 cup of the heavy syrup.
Add the drained peaches and frozen mango to the baking dish.
In a bowl, whisk together the 1/2 cup peach syrup, brown sugar, cornstarch, lemon juice, vanilla, cinnamon, and salt.
Pour this mixture over the peaches and mango and gently stir everything together.
Dot the top of the fruit with the 3 tablespoons of butter.
Bake the fruit mixture by itself for 10–12 minutes.
While it bakes, make the topping. In a large bowl, whisk together the flour, sugar, baking powder, and salt.
Cut the cold butter into the flour mixture until it resembles coarse crumbs with small pieces of butter throughout.
Mix the vanilla into the milk, then stir it into the flour mixture just until a soft dough forms. Don’t overmix. If the dough seems very dry, add 1–2 tablespoons more milk.
Remove the hot fruit from the oven and drop spoonfuls of the dough evenly over the top. It’s perfectly fine to leave some gaps where the fruit shows through.
If you’d like, sprinkle the top with the optional cinnamon-sugar mixture.
Bake for another 35–40 minutes, until the topping is golden brown and the fruit filling is bubbling around the edges.
Let it cool for 15–20 minutes before serving so the filling has time to thicken.