Sprinkle the remaining quarter cup of sugar evenly over the top of the frozen peaches. This final layer of sugar is what helps create that beautifully golden, very slightly crystallized surface on top of the finished cobbler. Do not skip it and do not stir it in.
Transfer the casserole dish carefully to the preheated oven. Bake for 55 to 70 minutes, until the top of the cobbler is deeply golden brown, the edges are crisp and pulling slightly away from the sides of the dish, and the peach filling is bubbling vigorously around the edges and through any gaps in the topping. The longer baking time compared to a fresh-fruit cobbler is necessary to account for the fact that your peaches started rock-hard and frozen — they need the full time to thaw, soften, and release all their juice into the dish.
When the cobbler is done, remove it from the oven and allow it to rest on a wire rack or heat-safe surface for at least ten minutes before serving. The filling will continue to thicken slightly as it cools, and the topping will remain crisp for a good twenty to thirty minutes out of the oven. Serve warm with vanilla ice cream or whipped cream.