Preheat the oven to 350 degrees F (175 degrees C). Spray a 9x5-inch loaf pan with cooking spray.
Sift flour, sugar, and rosemary together into a large mixing bowl. Pour in beer; stir to combine. Stir in apple and Cheddar cheese until well combined; batter will be stiff and sticky. Scoop batter into the prepared loaf pan.
Bake in the preheated oven until top is golden brown, 55 to 60 minutes. Remove from oven and pour melted butter on top. Return to oven and bake for another 3 to 5 minutes more.