Preheat oven to 400 degrees. Line a baking sheet with parchment paper.
Scoop seeds and stringy center portion of from squash and discard or reserve seeds for another use.
Place squash cut side up on baking sheet. Brush flesh with olive oil. Sprinkle with salt and pepper. Turn upside down.
Bake in preheated oven until tender, about 40 minutes.
Let cool slightly or use and oven mitt to hold squash, and shred spaghetti squash with a fork while leaving about 1/4-inch border. Set strings aside and return unfilled boats to baking sheet.
In a large saute pan melt butter over medium heat. Add garlic and flour and saute 1 minute.
While whisking vigorously slowly pour in half and half. Let cook, stirring constantly, until just thickened.
Reduce heat to low, add parmesan and stir until melted. If mixture seems too thick add in a splash or two of half and half. Season mixture with salt and pepper to taste.
Remove from heat. Add shredded spaghetti squash and 3/4 cup mozzarella cheese and toss to evenly coat (taste again for salt).
Divide mixture evenly among squash halves. Sprinkle with remaining 1/2 cup mozzarella cheese*.
Return to oven and bake until cheese has melted, about 10 minutes.
Sprinkle with parsley and serve warm.
*If you want squash to be easier to cut then follow this method:
Use a sharp knife to pierce holes in squash along where you will be halving, as if making a dotted around the squash (do not skip this step of piercing through skin or steam can build up and cause squash to burst!).
Place in microwave and cook for 5 minutes. Let cool slightly before removing from microwave.
Cut along dotted line and proceed as directed in step 1.
**Tip: If squash is tipping on one side (prior to second bake) prop it up with a strip of balled up aluminum foil underneath so filling doesn't spill out.