Preheat oven to 375 degrees F. Cut squash in half and scoop out the seeds and surrounding membrane. Lay squash flat on a baking sheet sprayed with cooking spray and bake until flesh is tender and can be easily scooped out using a fork, about 45-60 minutes. Set the squash aside to cool while you proceed with the rest of the recipe.
While the squash is cooking, diced up one large roasted pasilla or poblano pepper (or use something hotter if you prefer).
Heat 2 tablespoons butter and 3 tablespoons flour in a medium saucepan over medium high heat and cook for 3 minutes, stirring frequently.
Combine 1 3/4 cups milk and 1/4 cream and slowly pour into saucepan, whisking vigorously to avoid lumps. Add green chile peppers to the sauce and 1 3/4 cups of shredded Monterrey jack cheese. Salt and pepper to taste.
Let squash cool until you can handle it, then use a fork to scoop out all of the flesh and discard the shell. Notice how the flesh separates into strands like spaghetti?
Shred two cooked chicken breast halves with a fork and combine with the cream sauce and the squash and pour into a buttered 8 inch square baking dish.