Preheat the oven to 375°F. Set the squash in a pan and bake for 40 minutes. Turn it over and continue baking until completely tender, another 15 to 30 minutes. When done, turn off the oven and let the squash sit until needed.

Meanwhile, cut a sliver off the root ends of the onions. Boil them for 1 minute, then transfer to a bowl of cold water. Peel and cut any larger ones in half.

Heat 1 tbsp each oil and butter in a large skillet over medium heat. Add the onions, toss to coat, then sprinkle with sugar. Cook, giving the pan a shake now and then, until they start to color, after about 10 minutes. Add the parsnip, carrot, and herbs, season with salt and pepper, and continue cooking until the onions are nicely caramelized, about 10 minutes more.

Set the vegetables aside in a bowl, add another tbsp of oil to the pan, then add the garlic and mushrooms. Stir quickly, season with salt and pepper, and cook until they begin to color, about 5 minutes. Add the onions back to the pan and add the diluted tomato paste and soy sauce. Cook until the mushrooms are tender, then turn off the heat. (To keep the vegetables moist and to make a little sauce, add water or mushroom stock in small increments.)

Cut the cooked squash in half lengthwise and scoop out the seeds. Pull apart the strands with a fork, toss them with butter to taste, and season with salt and pepper.

Pile the squash onto four individual plates, spoon the vegetables around it, garnish with parsley, and serve.