Cook pasta in a Dutch oven according to package directions. Drain, return to Dutch oven, and keep warm.
Sprinkle chicken with 1 tsp. salt and 1/2 tsp. pepper. Dredge in flour.
Sauté chicken, in batches, in hot oil in a large skillet over medium-high heat 3 to 5 minutes on each side or until chicken is browned. Remove and keep warm.
Add onions, mushrooms, and garlic to skillet; sauté 5 to 7 minutes or until mushrooms are lightly browned. Stir in chicken broth and next 3 ingredients, and cook 3 to 5 minutes or until liquid is reduced by half, stirring to loosen particles from bottom of skillet.
Add mushroom mixture and spinach to pasta in Dutch oven, tossing to coat. Cook, covered, over medium-low heat 4 to 6 minutes or until greens are wilted. Spoon into a serving dish, and top evenly with chicken and Parmesan cheese.