1. Cook pasta according to package directions, omitting salt and fat; drain.
2. Heat a Dutch oven over medium-high heat; coat with cooking spray. Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper. Add chicken to pan; sauté 4 minutes, turning to brown on all sides. Add stock to pan; bring to a boil. Cook 2 minutes. Remove from heat; stir in 1/4 teaspoon salt, 1/4 teaspoon pepper, mascarpone, and 2 tablespoons parsley.
3. Preheat oven to 450°. Combine squash, shallots, garlic, and sliced shiitake mushrooms. Drizzle vegetable mixture with olive oil; toss. Transfer squash mixture to a small roasting pan; sprinkle with 1/4 teaspoon kosher salt and 1/4 teaspoon freshly ground black pepper. Bake at 450° for 20 minutes or until vegetables are just tender. Add vegetable mixture to pasta mixture; cook 1 minute or until thoroughly heated. Sprinkle with chives, 1/4 teaspoon kosher salt, and 1/4 teaspoon freshly ground black pepper.