Preheat the oven to 425 (220C) degrees. Line a large sheet pan with parchment paper.
Make the glaze:
Whisk all the ingredients in a small bowl.
Prepare the acorn squash:
To cut the squash, place it on a cutting board. Slice a thin piece off both the stem and bottom ends of the squash with a large knife. Stand the squash bottom side-down on the board so it's more stable. Cut it in half lengthwise. Scoop out the seeds with a spoon. Slice the squash into wedges 1/2-inch thick.
Put the slices on the prepared baking sheet and drizzle with the oil. Sprinkle with ½ teaspoon salt, turning to coat both sides of the squash. Lay them evenly, cut side down.
Roast the squash 15 minutes. Turn the slices over with a spatula or pair of tongs. Continue roasting another 10-15 minutes.
Take the sheet pan out of the oven. Turn on the oven broiler to high heat. Brush the glaze over the top of the squash and broil just until the squash is golden brown and the glaze is beginning to caramelize, 1-3 minutes depending on your broiler.
Cook the mushrooms:
While the squash is roasting, place a large (10-inch) non-stick skillet over medium-high heat. Add the oil, shallots and the mushrooms, stirring to coat in the oil. Cook undisturbed 3-4 minutes, until the mushrooms start to take on some color. Add the soy sauce, stir the mushrooms around and cook 1-2 more minutes, until softened. Remove from the heat and sprinkle with the pistachios.
To serve, transfer the squash to a large platter. Spoon the mushrooms over and around the squash.
Acorn squash skin is totally edible, but if you don't like the texture, use a swivel peeler to remove the skin before you slice it.