Heat oil in a large Dutch oven over medium heat. Add shallots and garlic; sauté 3 minutes. Add coconut milk and next 5 ingredients; bring to a boil. Add basil sprig. Reduce heat; simmer, uncovered, 15 minutes.

Add mussels; cover and simmer 10 minutes or until shells open. Remove from heat; discard any unopened shells. Place mussels in wide, shallow bowls; ladle broth over mussels. Sprinkle with chopped basil.