Preheat oven to 425° F. Microwave each spaghetti squash for 2-4 minutes in the microwave to soften them (the amount of time will depend on how large they are and how difficult they are to cut into). Cut spaghetti squash in half then scrape out seeds. Drizzle with olive oil, season with salt and pepper then bake in the oven for 25 minutes.
Remove from oven and scrape out flesh using a fork. It won't be cooked through and it doesn't have to be perfect, even if you just get a little bit up the rest will come up during cook time. Top each spaghetti squash with raw chicken, then place back in the oven another 10 minutes.
Meanwhile, make balsamic glaze (if not using storebought) by bringing balsamic vinegar and brown sugar to a boil over medium heat. Simmer for 10 minutes on med-low heat until it reduces and thickens.
Remove spaghetti squash from oven again, and add cherry tomatoes and bocconcini cheese. Bake another 10 minutes until cherry tomatoes start to burst and cheese is melted.
Remove from oven, generously top with fresh basil leaves, then drizzle with balsamic glaze. Serve and enjoy!