1. Preheat your oven to 400 F (200 C). Carefully cut the spaghetti squash in half lengthwise. Scoop out the seeds and stringy bits from the center. Drizzle the cut sides with a little olive oil, season with salt and pepper, and place them cut-side down on a baking sheet. Roast for 30-40 minutes, or until the flesh is tender when pierced with a fork.

2. While the squash roasts, heat 1 tablespoon of olive oil in a large skillet or Dutch oven over medium-high heat. Add the cubed chicken and cook, stirring occasionally, until browned on all sides and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.

3. In the same skillet, add the chopped onion and cook until softened, about 3-4 minutes. Stir in the minced garlic and cook for another minute until fragrant. Add the broccoli florets and chicken broth to the skillet. Bring to a simmer, then cover and cook for 5-7 minutes, or until the broccoli is tender-crisp.

4. Return the cooked chicken to the skillet with the broccoli mixture. Stir in the Italian seasoning, salt, and pepper. Mix well to combine all the flavors.

5. Once the spaghetti squash is tender, carefully remove it from the oven. Using a fork, gently scrape the flesh away from the sides of the squash, creating spaghetti-like strands. Leave the strands in the squash halves; do not remove them completely.

6. Spoon the chicken and broccoli mixture evenly into the two spaghetti squash halves. Sprinkle 3/4 cup of mozzarella cheese and all of the Parmesan cheese over the filling in each squash half. Return the stuffed squash to the oven and bake for another 10-15 minutes, or until the cheese is melted and bubbly and the filling is heated through.

7. Carefully remove the stuffed spaghetti squash from the oven. Let it cool for a few minutes before serving directly from the squash halves.