To cook the Spaghetti Squash
Preheat oven to 400 degrees F and line a large baking sheet with parchment paper.
Scrub the squash clean and dry thoroughly. Cut the squash in half lengthwise using a sharp, stable and reliable knife. Scoop out the seeds.
Drizzle the squash with olive oil and use a pastry brush (or your hands) to brush over the entire surface of the squash. Sprinkle with salt and pepper and place cut-side down on the lined baking sheet.
Place squash in the oven and bake for 45 minutes to 1 hour or until squash is tender when pierced with a fork.
When cool enough to handle, gently scrape out the squash with a fork to remove the flesh in long strands.
To Poach the chicken
Bring a large pot of water to a boil over high heat. Add the chicken to the pot and return the water to a rolling boil. Remove from heat, cover, and set aside to "poach" (cook) for approximately 25-30 minutes. Carefully remove chicken from the pot and set aside to cool before shredding.
For the twice-baked spaghetti squash
Preheat oven to 350 degrees F.
Add one tablespoon of olive oil to a large skillet over medium-high heat. Add the shallots and cook for 4-5 minutes, stirring often. Reduce heat to low and stir in the minced garlic and Italian seasoning. Mix well to combine. Cook for 60 seconds, stirring constantly.
Add the tomatoes and splash of white wine or chicken broth. Mix well and add the shredded chicken to the skillet. Continue to cook until the tomatoes have burst. Remove from heat and set aside.
In a large mixing bowl mix together the ricotta, mascarpone, cheddar cheese, half the mozzarella cheese, and chopped parsley.
Once the chicken and tomatoes have cooled slightly, mix to combine with the cheese mixture. Season with additional salt and pepper, to taste.
Transfer the cooked strands of spaghetti squash to the mixing bowl with the cheese and chicken. Gently mix to combine.
Evenly divide spaghetti squash and chicken mixture between the spaghetti squash bowls. Top with mozzarella cheese (or cheese of choice) and place face up on the prepared baking sheet. Cover the baking dish and squash with foil, creating a tent to prevent the foil from touching the cheese.
Bake at 350 degrees for 15 minutes. Remove the foil tent and bake an additional 5-10 minutes, or until cheese is golden and bubbly.