Melt butter/margarine in large skillet over medium-high heat and cook mushrooms and onion, stirring occasionally, 5 minutes or until vegetables are golden. Reduce heat to medium.
Stir in garlic and flour and cook, stirring constantly, 2 minutes.
Whisk in broth and Hellmann's Mayonnaise; bring to a boil. Reduce heat and simmer, stirring occasionally, 2 minutes or until thickened.
Stir in turkey, linguine, peas and cheese and cook 2 minutes or until heated through. Season, if desired, with salt and pepper.