Preheat oven to 375°F.
Make the filling: In a large bowl, toss the berries with sugar, cornstarch, lemon juice, vanilla, and salt until evenly coated. Transfer to an 8x8 or 9x9 baking dish and spread in an even layer.
Make the topping: In a separate bowl, whisk the gluten-free flour, sugar, baking powder, and salt. Add the dairy-free milk, melted dairy-free butter, and vanilla. Stir just until you get a thick, pancake-like batter.
Assemble: Spoon the batter over the berries in rustic dollops. Don't fully cover the fruit — gaps let the berries bubble through.
Bake: 35–40 minutes, until the topping is golden and the filling is bubbling thickly at the edges.
Rest: Let cobbler rest 10–15 minutes before serving so the filling sets up.