Place butter in a 1 1/2-quart baking dish and put in the oven to melt. Preheat the oven to 350 degrees F (175 degrees C).
Remove melted butter from the oven and set aside to cool, about 5 minutes.
Mix flour, sugar, milk, and 1 teaspoon cinnamon together in a bowl. Gently pour batter into the middle of the melted, cooled butter; be sure you do not stir. Pour peaches and juice into the center of the batter; once again it is important you do not stir. Sprinkle cinnamon on top, a little at a time.
Bake in the preheated oven until brown and bubble, 30 to 60 minutes; cooking time will vary depending on the wetness of the ingredients.