Preheat oven to 375°F (190°C).
Using fork, pierce squash all over. Roast in roasting pan in oven until tender when pressed, 1hour and 15 minutes, turning a couple of times. Turn off oven.
Meanwhile, trim onions. Blanch in saucepan of boiling water for 1 minute. Using slotted spoon, remove to bowl of ice water to stop cooking process. Peel; cut any large ones in half.
In large skillet, heat 2 tablespoons (25 mL) of the oil over medium heat. Cook onions and sugar, stirring often, for about 15 minutes or until onions are starting to turn golden.
Stir in celery, carrot and the thyme and sage; add red pepper, half of the salt and pepper, cook, stirring often, for 10 minutes or until onions are a deep caramel colour. Transfer to bowl.
Add 2 tablespoons (25 mL) of the oil to skillet. Stir in mushrooms and garlic; cook, stirring for about 10 minutes or until excess liquid has evaporated and mushrooms are starting to turn golden brown.
Return onion mixture to pan along with stock, soy sauce, vinegar and tomato paste; cook for 5 minutes. Meanwhile, stir butter with flour; add to pan and cook, stirring gently, until completely melted and sauce is thickened.
Cut squash in half lengthwise and scoop out seeds. Using fork, pull apart strands and place in bowl. Add remaining oil, salt and pepper; toss to coat. Mound on plates; spoon ragout over top. Garnish with parsley.