Preheat the oven to 350°F. Place the stick of butter in a 10-inch casserole dish or cast-iron skillet and place it in the oven while it preheats. Allow the butter to melt while you prepare the remaining ingredients.
Once the butter has melted, carefully remove the baking dish from the oven. Pour the melted butter into a mixing bowl and set the baking dish aside.
Add the sugar, flour, baking powder, salt, milk, and vanilla to the melted butter. Stir until everything is well combined and you have a smooth batter.
Pour the cake batter into the baking dish.
Spoon the pie filling into the baking dish over the batter.
Bake at 350°F for 30–40 minutes, or until the cake is golden brown and cooked through.
Let the cobbler cake rest for a few minutes before serving. Serve warm, as-is or with a scoop of vanilla ice cream.