Cook the Spaghetti Squash:
Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Scrub the spaghetti squash clean and dry thoroughly. Cut the squash in half lengthwise, from stem to end, using a sharp knife. Scoop out the seeds.
Drizzle the squash halves with olive oil and brush evenly over the surface. Sprinkle with salt and pepper, then place cut-side down on the prepared baking sheet.
Bake for 45 minutes to 1 hour, or until the squash is tender when pierced with a fork.
Once cool enough to handle, scrape the flesh of the squash with a fork to create long strands. Set aside.
Prepare the Chicken and Broccoli:
Preheat the oven to 350°F (175°C).
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the chopped chicken, season with salt and pepper, and cook for 5-6 minutes until browned, stirring often. Remove the chicken from the skillet and set aside.
Return the skillet to medium heat, add another tablespoon of oil, and sauté the minced shallots for 2-3 minutes until softened. Add the garlic, salt, pepper, and Italian seasoning, cooking until fragrant (about 30 seconds).
Stir in the broccoli florets and 1-2 tablespoons of water. Cover and steam the broccoli for 2 minutes, then uncover and stir in the chicken. Cook for an additional 1-2 minutes, stirring often. Remove from heat.
Mix the Filling:
In a large mixing bowl, combine the cream cheese and Greek yogurt until smooth. Add the cooked chicken and broccoli mixture, stirring to combine.
Stir in the Parmesan cheese and half of the shredded mozzarella.
Transfer the spaghetti squash strands to the bowl with the chicken and broccoli mixture. Gently mix to combine all the ingredients.
Assemble and Bake:
Divide the filling mixture evenly between the spaghetti squash shells (squash boats). Top each with the remaining mozzarella cheese.
Place the filled squash halves on the prepared baking sheet. Cover with foil, tenting it to prevent the foil from touching the cheese.
Bake at 350°F for 15 minutes, then remove the foil and bake for an additional 5-10 minutes, or until the cheese is golden and bubbly.
Serve:
Garnish with fresh chopped parsley or red pepper flakes if desired. Serve warm and enjoy!