Preheat oven to 400 F. Microwave spaghetti squash for 2 min to soften, then slice in half lengthwise. Scoop out seeds, then drizzle with 1 tsp olive oil, season with salt & pepper and bake for 40 min.
Meanwhile, heat remaining tsp olive oil in a large skillet. Saute chicken until browned, then remove from heat and set aside.
Wipe pan clean, then melt butter. Saute garlic for 30 seconds until fragrant. Whisk in flour until thickened, then whisk in chicken broth and cream, bringing to a boil. Stir in parmesan cheese and remove from heat.
Remove spaghetti squash from oven, and scrape with a fork to make strands. Add chicken and broccoli overtop, then divide alfredo sauce among squash halves. Top with mozzarella cheese, then bake another 10 minutes until cheese has melted.
Remove from oven, garnish with parsley then serve and enjoy!