Heat oil in Dutch oven over medium heat. Add shallots; cook and stir about 5 minutes or until crisp and browned. Remove shallots; set aside. Using vegetable peeler, remove zest from lime in strips; cut lime in half. Add garlic, ginger, and curry paste to Dutch oven; cook and stir 1 minute. Add broth, water, and fish sauce. Squeeze juice from lime into broth; add strips of zest. Bring to boiling.
Stir in shrimp and noodles. Return to boiling; reduce heat. Cook 3 to 4 minutes or just until shrimp turn opaque. Stir in coconut milk; heat through. Remove lime zest. Top bowls with shallots and basil; serve with lime wedges.