Roast Acorn Squash:

Preheat oven to 400°F.
Slice each acorn squash in half down the middle. Keep fingers away from the knife to avoid injury. Use a spoon to scoop out the seeds and fleshy strands tangled with the seeds.
Place acorn squash cut sides up on a baking sheet. Drizzle the cut sides with olive oil and rub the oil into the squash. Season generously with salt and pepper. Turn the squash over, and place it cut sides down on the baking sheet.
Roast in the preheated oven at 400°F for 30 minutes.
Make Spinach and Cheese Mixture:

In a medium skillet, heat olive oil on medium heat and add fresh spinach. Cook for about 5 minutes until the spinach wilts. If there is any liquid in the pan, drain it.
Add cream cheese to a microwave-safe large-sized bowl. Soften the cream cheese briefly in the microwave oven. Ensure the cheese does not actually melt, just softens.
Add shredded Parmesan and cooked spinach to the same bowl. Mix everything well.
Stuff Acorn Squash:

By this time, you have roasted the acorn squash for 30 minutes. Remove them from the oven and turn cooked squash halves cut sides up.
Divide the spinach and cheese mixture among the 4 halves and stuff the squash until the mixture is leveled.
Sprinkle the cheese mixture with half of the fresh thyme.
Roast the stuffed acorn squash in the preheated oven at 400°F for 20 more minutes until the cheese mixture melts.
Broil for 3 to 5 minutes to get a golden crust over the cheese. Watch closely and be very careful not to burn the squash and the cheese mixture.
Top with freshly ground black pepper and fresh thyme.