Preheat oven to 425 degrees F. Cut the top and a sliver off the bottom so that the squash can sit flat. Scoop out seeds. Brush with 1 tablespoon olive oil and sprinkle with salt and pepper. Place face down on aluminum foil lined cookie sheet.
Bake squash for 35-45 minutes depending on size, or until squash is tender.
In a large skillet over medium heat, add olive oil and garlic. Saute for 1-2 minutes, until the garlic is golden and fragrant.
Reduce heat to low and add cornstarch. Immediately whisk until it makes a thick paste.
Add broth and milk, stirring between additions.
Add cream cheese and sour cream. Stir until combined and smooth. Add salt and pepper to taste.
Add spinach and simmer 3-5 minutes, or until the spinach wilts.
Divide the spinach filling evenly between the squash halves. Top each halve generously with mozzarella and Parmesan.
Turn oven to broil. Broil the squash halves, face up, for 3-5 minutes, or until the cheese starts to bubble and turn golden brown. Serve immediately and enjoy!