Preheat your oven to 350°F. Place the butter in a 9x9-inch baking dish and let it melt in the oven for about 5 minutes.
In a bowl, whisk together the flour, brown sugar, granulated sugar, cinnamon, baking powder, and salt. Stir in the milk and vanilla extract until just combined.
Remove the baking dish from the oven. Pour the batter evenly over the melted butter without stirring. Spoon the cherry filling evenly over the top (don't stir).
Bake in the preheated oven for 45 minutes or until the top is lightly golden and the filling is bubbly.
Allow the cobbler to cool for 10 minutes before serving. If desired, top with a scoop of ice cream or a dollop of whipped cream for garnish.