Preheat oven to 350 degrees. Use a fork to stab holes all over the squash. Place on a baking sheet and cook in the oven for 1 hour, or until soft.
Meanwhile, bring a large pot of salted water to a boil. Score a small X in the bottom of each tomato and place in the boiling water. Blanch for 1 minute. Remove the tomatoes and place in a large bowl filled with ice water until cool to the touch. Gently peel with a small knife, starting at the X. Purée the peeled tomatoes in a blender or food processor until smooth. Alternately, for a chunkier sauce, gently smash with a potato masher.
Heat 2 tablespoons oil in a large pot over a high flame until hot. Add onions, carrots and celery, and season with a pinch of salt. Cook for 10 minutes, stirring occasionally. Add mushrooms and season with a pinch of salt. Cook until wilted and slightly browned, about 12 minutes. Add garlic and stir to combine. Continue cooking for another 3 minutes. Add tomato purée, sugar and a pinch of sea salt. Bring to a simmer and reduce heat to low. Stir often, cooking until the sauce thickens, about 30 minutes.
Cut squash in half and scoop out the seeds. Scrape the inside flesh with a fork to resemble spaghetti. Divide between 2 plates and top with the Mushroom Bolognese.