Serve this with a big dollop of sweetened whipped cream or Brennan's Vanilla Ice Cream.
Preheat the oven to 350 degrees F (175 degrees C). Place the butter in a 9 X 13 inch baking dish, and place in the oven to melt while the oven is preheating. Remove as soon as butter has melted, about 5 minutes.
In a medium bowl, stir together 1 cup flour, 1 cup sugar, and baking powder. Mix in the milk until well blended, then pour the batter into the pan over the butter. Do not stir.
Rinse out the bowl from the batter and dry. Place cherries into the bowl, and toss with remaining ¾ cup of sugar and 1 tablespoon of flour. Distribute cherry mixture evenly over the batter. Do not stir.
Bake for 50 to 60 minutes in the preheated oven, until golden brown. A toothpick inserted into the cobbler should come out clean.