1. Prepare noodles according to package directions. Drain.
2. Combine 3 tablespoons water and next 4 ingredients (through cornstarch) in a small bowl, stirring with a whisk. Set aside.
3. Combine red pepper, black pepper, and shrimp in a medium bowl; toss to coat.
4. Heat a wok or a large skillet over high heat. Add 1 1/2 teaspoons oil to pan; swirl to coat. Add shrimp mixture; cook 3 minutes or until shrimp are almost done, turning once. Remove shrimp mixture from pan. Add remaining 1 1/2 teaspoons oil to pan; swirl to coat. Add onion, bell pepper, and ginger; cook 2 minutes, stirring occasionally. Return shrimp mixture and juice mixture to pan. Add mango; cook 1 minute or until liquid thickens slightly and shrimp are done. Sprinkle with basil. Serve over noodles.