Preheat the oven to 500°.
Halve the onions legthwise, discarding the papery skin as well as the layer beneath if it's tough or dry. Trim the tops and a little off the bottom (not too much - you want to ensure the onion halves stay held together at the base.)
In a medium bowl, whisk together the melted butter, miso, and warm water until fully combined.
Place the onion halves, cut side down and spaced apart, in a 9x13baking dish and pour the miso water over them.
Cover the dish tightly with aluminum foil and bake for 35 minutes, then remove the foil and turn the onions over so they are cut-side up (take care to ensure they remain intact).
Baste the onions very well with the miso water in the bottom of the pan.
Return the pan to the oven, uncovered, for another 60-75 minutes, basting every 10 minutes, until the onions are very soft, deeply browned on top, and the sauce has reduced to a gravy consistency.
Carefully transfer the onions to a platter, pouring the sauce over and around them, and serve at once.