Preheat oven to 400 degrees F. Brush cut sides of squash with oil, and sprinkle with salt and pepper to taste. Place squash, cut sides down, on a rimmed baking sheet. Bake until tender, about 45 minutes.
While the squash is baking, make the creamy roasted red pepper sauce. Roast red peppers over gas flame, under the broiler, or on the grill. Roast for about 10 minutes, or until peppers are completely black. Place peppers in a paper bag to allow to sweat. Peel the charred skins from the peppers and remove the seeds. Chop the peppers and set aside.
In a large saucepan, heat the olive oil over medium heat. Add onion and sauté until softened, about 3 minutes. Stir in garlic and cook for 2 minutes. Add the red peppers and diced tomatoes. Add oregano, red pepper flakes, fresh basil, and season with salt and pepper. Simmer on stove for 10 minutes. Stir in the Greek yogurt. Purée the sauce in the pan, using an immersion blender. You can also transfer the sauce to a blender or food processor, but be careful. Make sure the sauce is not super hot so you don't get burnt. Puree until smooth, with some texture remaining.
When the squash is done baking, let it cool for a few minutes-until you can touch it. Scrape the squash with a fork to remove flesh in long strands. Place in a large bowl or on individual plates. Top spaghetti squash with the creamy roasted red pepper sauce and serve warm.