Preheat to 425°. Halve squash lengthwise and scoop out seeds with a large spoon. Using a peeler, remove skin and white flesh below (you should reach the deep orange flesh). Rub all over with oil; season with salt and pepper. Roast in a baking dish just large enough to hold halves side by side until beginning to soften, 15–18 minutes.
Meanwhile, combine the ginger with miso, walnut oil, walnuts, soy sauce, either in a high-speed blender until just combined.
Transfer squash to a cutting board and let cool slightly. Using a sharp knife, score rounded sides of squash halves crosswise, going as deep as possible but without cutting all the way through. Return squash to baking dish, scored sides up and season with salt and pepper.
Roast squash, basting with miso walnut sauce every 10 minutes or so and using pastry brush to lift off any glaze in dish that is browning too much, until tender and glaze forms a rich brown coating, 45–60 minutes.