Preheat your oven to 400°F (200°C). Cut the spaghetti squash in half lengthwise, scoop out the seeds, and brush each half with olive oil. Place them cut side down on a baking sheet lined with parchment paper.

Heat one tablespoon of olive oil in a large skillet over medium heat. Add minced shallots and garlic, sautéing until fragrant. Then add chopped chicken breasts along with salt, black pepper, and Italian seasoning. Cook until the chicken is golden brown and cooked through.

Stir in broccoli florets and cook for another few minutes until they are tender yet still vibrant green.

In a large bowl, combine cream cheese, Greek yogurt, Parmesan cheese, and mozzarella cheese until smooth. Fold in the chicken-broccoli mixture gently until everything is well coated.

Once your spaghetti squash halves are roasted and cool enough to handle, use a fork to scrape out some of the flesh. Mix this flesh into your filling mixture before spooning it back into each squash half generously.

Place filled squash halves back onto your baking sheet and sprinkle any remaining mozzarella cheese on top. Return them to the oven for an additional 20 minutes or until everything is bubbly and golden brown.