Heat olive oil in large skillet over medium heat. Add garlic; sauté 1 to 2 minutes or until tender. Stir in leeks; cook 10 minutes, stirring occasionally and adding small amounts of vegetable broth at a time.
Stir in shrimp and wine; bring to a simmer. Cook 5 to 6 minutes, stirring occasionally, until reduced slightly. Season with salt and pepper.
Cook Fettuccine according to package directions, adding green beans during last 5 minutes of cook time. Drain and return to pot.
Add shrimp mixture to hot Fettuccine; toss.
Transfer to serving platter; sprinkle with grated cheese and parsley.
