Preheat your oven to 400°F. Carefully slice each butternut squash in half lengthwise and scoop out the seeds and any fleshy strands. Place the squash halves cut-side up on a baking sheet; drizzle and rub the cut sides with 2 tablespoons olive oil. Season generously with 1/4 teaspoon salt and some freshly ground black pepper. Turn the squash halves over onto the baking sheet, cut sides down. (Lining the baking sheet with parchment paper makes for easy clean-up.) Roast in the oven for 40 minutes.
While the butternut squash is roasting, heat 1 tablespoon olive oil in a medium skillet over medium heat. Add the fresh spinach leaves and cook for about 5 minutes, stirring occasionally, until the spinach is wilted. If any liquid accumulates in the pan, drain it before proceeding.
Place the cream cheese in a large, microwave-safe bowl and briefly soften it in the microwave—just until it's mixable, not melted. Add the wilted spinach from Step 2, 1 cup shredded Parmesan cheese, and half of the cooked, chopped bacon. Mix everything together until well combined. I like to reserve the other half of the bacon for topping the stuffed squash later for texture and flavor.
After roasting, remove the squash from the oven and let cool slightly. Carefully turn the squash halves cut-side up. Using a spoon, scoop out most of the flesh, leaving about a 1-inch border along the sides to help the shells hold their shape. Divide the bacon-cheese-spinach mixture from Step 3 among the four squash halves, stuffing and leveling the mixture. Top each half with the reserved bacon pieces for extra crunch and flavor.
Return the stuffed squash halves to the oven at 400°F and roast for another 15 minutes, until the cheese mixture is melted through. Optionally, broil the stuffed squash for 3–5 minutes to create a golden crust on top. Broil on the second rack from the top and watch closely, as every oven is different—I find 5 minutes is just right for some caramelized color. When done, remove from the oven and immediately top with fresh thyme and a little extra ground black pepper for a fresh finish.