Preheat the oven to 400 degrees Fahrenheit.
Cut the spaghetti squash in half lengthwise. Scoop out the seeds.
Pour 1 tsp of olive oil on each half.
Place the spaghetti squash face down in a glass baking dish.
Cook for about 30 minutes, depending on size of the spaghetti squash, it's done when the skin becomes tender.
Meanwhile, in a medium pot on medium heat, add 1 cup of pumpkin puree, and one cup of milk and 1/2 tsp of pumpkin spice, and salt. Mix until incorporated.
Add cheese to the pot. Continue to mix until the cheese gets incorporated. If the sauce needs to be thickened add the tsp of cornstarch.
When the spaghetti squash is done, shred spaghetti squash and add it to the pumpkin and cheese mixture. Mix until all the squash is covered with pumpkin cheese sauce.