Preheat the oven to 425 degrees F. Cut the squash in half lengthwise using a serrated knife and remove the seeds with a spoon. Brush the flesh of both halves with 1 teaspoon oil and season with 1/2 teaspoon salt and a few grinds of pepper. Put the halves flesh-side down on a baking sheet and cook until tender, the flesh can easily be flaked with a fork and the edges just turn brown, about 45 minutes. Separate the strands of squash by scraping the flesh with a fork. Leave the scraped strands inside the squash.
Meanwhile, heat the remaining oil in a large skillet over medium-high heat. Add the sausage and cook, breaking it up with a wooden spoon and taking care to keep some larger chunks, until it just starts to brown and crisp up, 5 to 6 minutes. Add the tomatoes, thyme, red pepper flakes and garlic and cook, stirring, until just fragrant, about 1 minute. Pour in the wine and cook until reduced by half, 2 to 3 minutes. Add the heavy cream and 1 teaspoon salt and bring to a boil. Lower the heat to medium and simmer until the sauce reduces by half, 3 to 4 minutes. Add the white beans and spinach to the skillet and cook, stirring frequently, until the spinach just wilts and is still vibrant green, 1 to 2 minutes.
Divide the sausage mixture between the 2 squash halves and mix with the squash strands until well combined. Sprinkle each squash half with 1 tablespoon Parmesan and serve with more red pepper flakes, if using.
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