Place potatoes in 2-quart saucepan, add enough water to cover potatoes. Heat to boiling, reduce heat. Cover and simmer 20 to 30 minutes until potatoes are tender, drain. Shake pan with potatoes over low heat to dry (this will help mashed potatoes be fluffier).
With a potato masher, mash potatoes in pan until no lumps remain. Add broth in small amounts, mashing after each addition.
Add oil, rosemary, salt, and cheese. Mash vigorously until potatoes are light and fluffy. Cover and let stand 5 minutes. Sprinkle with additional rosemary and Parmesan cheese (optional).