Place the first five ingredients in a blender; cover and process until blended. Remove 1 tablespoon mixture; toss with shrimp.
Cook pasta according to package directions. Meanwhile, in a large nonstick skillet, heat 2 teaspoons oil over medium-high heat. Add half of the shrimp mixture; stir-fry 2-4 minutes or until shrimp turn pink. Remove from pan; keep warm. Repeat with remaining oil and shrimp mixture.
Add broth, coconut milk, salt and remaining basil mixture to same pan. In a small bowl, mix cornstarch and water until smooth. Stir into broth mixture. Bring to a boil; cook and stir 1-2 minutes or until slightly thickened. Stir in lime zest.
Drain pasta; add pasta and shrimp to sauce, tossing to coat.