For mango-basil vinaigrette: Place 1/2 cup of the mango in a food processor or blender. Cover and process or blend until smooth. Add salad dressing, basil, mint, and crushed red pepper; cover and process or blend just until mixed. Let stand for 5 minutes for flavors to develop.
Divide greens evenly among six salad plates. Top greens with the remaining mango, breaking mango into bite-size pieces. Drizzle each plate with 2 tablespoons of the mango-basil vinaigrette. Top with cheese. Serve immediately.