Prepare pasta according to package directions, omitting salt and fat.
While pasta cooks, combine flour and next 4 ingredients in a large bowl. Slowly whisk in broth and milk.
Melt butter in a large nonstick skillet over medium-high heat. Add mushrooms, onion, and celery; cook, stirring constantly, 6 minutes or until almost all liquid is absorbed and onion is tender. Stir in broth mixture; bring to a boil, reduce heat, and cook, stirring constantly, 4 minutes or until thick and bubbly. Add chicken and peas; cook 3 minutes or until thoroughly heated, stirring occasionally. Stir in parsley. Serve over hot cooked pasta.