Preheat oven to 500f.
In a 9” x 13” x 2” rectangular baking dish, add miso paste and melted butter. Whisk until smooth.
Whisk in the warm water.
Halve onions lengthwise. Trim a little off the tops and bottoms but leaving enough at the base to ensure they remain intact through cooking. Remove all layers with papery skins.
Arrange halved onions in baking dish, cut-side down in a single layer. Cover tightly with foil and bake 20 minutes.
Remove foil. Carefully turn over onions so they are cut-side up. Baste onions with liquid in the dish.
Return to oven and bake uncovered a further 30-40 minutes or until onions are tender and browned at the edges, basting every 10 minutes.
About 10 minutes before onions are ready, blanch green beans. Bring a large pot of water to a boil and salt like you would for pasta.
Prepare an ice bath on the side. Blanch green beans around 2-4 minutes or whenever they are crisp-tender and still bright green.
Drain in colander and immediately transfer into ice bath to stop the cooking. Drain well and place in an oven-safe shallow serving dish. Toss with a little oil.
When onions are ready, remove from the oven and turn heat down to 350f. Place the green beans in the oven to heat back through.
Decide whether the onion sauce consistency needs to be adjusted. Pour braising liquid into a small pot and bring to a gentle simmer.
Whisk in a little of the cornstarch slurry and cook until sauce has thickened as desired.
To serve, remove green beans from the oven, arrange braised onions on top and pour sauce over everything.
