Preheat your oven to 375°F (190°C) and position a rack in the middle. Butter or spray your baking dish.
Combine the rhubarb and strawberries in a large bowl. In a separate small bowl, whisk together sugar, cornstarch, and salt, then sprinkle over the fruit. Add lemon juice and vanilla, then gently toss until everything is evenly coated.
Transfer the fruit mixture to your prepared baking dish, spreading it out evenly. If the fruit has released a lot of juice, leave some behind to prevent a soggy cobbler.
For the topping, whisk together the flour, sugar, baking powder, baking soda, and salt in a medium bowl. Add the cold butter pieces and use a pastry cutter or your fingertips to work it into the flour until the mixture resembles coarse crumbs with some pea-sized butter pieces remaining.
Combine the buttermilk and vanilla, then pour into the flour mixture. Stir just until a shaggy dough forms – overmixing will make the topping tough!
Drop spoonfuls of the dough over the fruit mixture, leaving some gaps for the filling to bubble through. Don’t worry about covering the entire surface – the dough will spread as it bakes.
Sprinkle the remaining tablespoon of sugar over the topping for a beautiful sparkly finish and extra crunch.
Bake for 40-45 minutes until the topping is golden brown and the filling is bubbling around the edges. If the top browns too quickly, loosely cover with foil for the remaining baking time.
Let the cobbler cool for at least 20 minutes before serving to allow the filling to set up slightly. The cobbler is best enjoyed warm with a scoop of vanilla ice cream or a dollop of whipped cream.