Preheat your oven to 350°F (175°C). Place the rack in the center of the oven.
Wash and prepare your chosen fruit. Slice larger fruits such as peaches, apples, pears, or plums into bite-sized pieces.
Place the fruit in a bowl and toss gently with sugar, lemon juice, and vanilla. If using particularly juicy fruit, add cornstarch to help thicken the filling.
Pour the melted butter into a 9 × 13-inch baking dish. Do not stir it into the batter. The butter will help create the delicious golden edges and bottom of the cobbler.
In a large bowl, whisk together the flour, sugar, baking powder, and salt.
Pour the batter evenly over the melted butter.
Gently spoon or distribute the prepared fruit over the top of the batter. Again, avoid stirring. As the cobbler bakes, the batter will rise around the fruit.
The cobbler is ready when the top is golden brown, the edges are slightly crisp, and the center is set.
Remove the cobbler from the oven and let it rest for about 10–15 minutes. This allows the fruit juices to settle and the batter to firm up slightly.
Spoon the warm cobbler into bowls and top with vanilla ice cream or whipped cream.