Preheat oven to 400 degrees.
To soften the squash before cutting, microwave whole for 4-5 minutes. Be careful when removing, skin will be hot. Trim both end off the squash and cut lengthwise down the middle making two boats. Scrape and scoop seeds out and discard.
Drizzle the cut side of squash with olive oil and sprinkle with salt. Place cut side down on parchment lined sheet pan and roast at 400 for about 30 minutes or until tender.
While the squash is in the oven, melt butter in large skillet. Add onion, bell pepper, celery, poblano and cook over medium high heat for about 7 minutes or until softened. Throw in garlic cook for another 1-2 minutes. Add chicken stock and tomatoes and chilis and continue to cook till stock is reduced by half. You should have about 3 tablespoons of liquid left. Add the cream to the veggies and simmer till reduced and thickened. Remove from heat and place veggie mixture in a large mixing bowl.
Add cream cheese, salt, pepper, garlic, and cumin. Stir till combined and cream cheese is melted.
After 30 minutes, remove squash from oven and carefully flip over. The squash should be tender on top but not completely done all the way through. Using a fork remove the spaghetti squash from the peel. If there is excess moisture from the cooked squash, you will want to place the squash on some paper towels to remove the moisture.
Lower the oven temperature to 350 degrees. Gently mix the squash into the veggie mixture. Then, gently stir in 1/2 cup of the shredded cheese and the chicken.
Put the squash and chicken mixture into a greased casserole dish or 9x13 pan. Top with remaining cheese and bake at 350 for 20 minutes or until warmed through and cheese is melted and bubbly. Let sit 10 minutes before digging in!