Preheat oven to 375F.
Cut the spaghetti squash in half crosswise. Sprinkle with some olive oil, salt and pepper. Place the squash cut side down on a baking dish and roast for 30 to 45 minutes. A shorter roast will give you a crunchier, al dente texture, while a longer, 45-minute roast will result in a very soft texture. Remove from the oven and set aside to cool down a little.
Meanwhile, heat the butter over medium heat in a large sauce pan. Add the onion and garlic and saute them for 1 minute, until they become fragrant. Add the carrot, red bell pepper and zucchini and cook, stirring, for about 5 minutes, until the vegetables have softened up. After that, add the flour and stir thoroughly until it's well incorporated. Pour in the milk, constantly stirring. Add the thyme and cook for about 5 minutes or until the mixture begins to boil. At this point, stir in the shredded cheese and mustard. Add one 1 teaspoon of salt and 1/4 tsp of black pepper. Stir and taste for salt. Add more if needed. Remove from heat and stir until the cheese has fully melted.
Insert the squash halves cut site up into 4-inch ramekins. Ladle the cheese sauce into spaghetti squash halves, garnish with chopped parsley and Parmesan cheese and serve.
Alternatively, using a large spoon, scoop out spaghetti squash flesh into a bowl. Add the cheese sauce, mix, then spoon back into shells. Top with chopped parsley, grated Parmesan cheese and serve.