Preheat your oven to 350 degrees Fahrenheit (175 degrees Celsius). Do not wait for the oven to finish preheating before you get started — you will be melting the butter in the dish while the oven comes up to temperature, and timing it correctly is part of what makes this method work so cleanly.
Place the stick of butter, whole and still cold, directly into a 9-by-13-inch casserole dish. Slide the dish into the oven as it preheats. Watch it carefully and remove the dish as soon as the butter is completely melted and just beginning to foam at the edges. You do not want the butter to brown at this stage. Set the dish aside on a flat, heat-safe surface.
While the butter is melting, make your batter. In a large bowl, whisk together the flour, three-quarters of a cup of the sugar, and the whole milk until the batter is completely smooth and free of lumps. This is a thin, pourable batter — that is exactly what you want. Do not add any leavening agents or anything else. The simplicity of the batter is what creates that distinctive cobbler texture: dense and slightly doughy in the center where it meets the fruit juice, and beautifully crisp and golden at the edges where it meets the buttered sides of the dish.
Pour the batter gently and evenly over the melted butter in the casserole dish. Do not stir. Do not mix the batter into the butter. Simply pour it over the top and let it spread naturally. It will not cover the butter completely at first and that is completely fine.
Now scatter the rock-hard frozen peach slices evenly over the top of the batter. Again, do not stir. Do not press them down. Simply distribute them as evenly as you can across the surface of the batter and let them rest there. They will sink naturally as they bake and release their juice, and the batter will rise up around them in the way that makes cobbler cobbler.
