Place chiles, cut sides down, on a foil-lined baking sheet; broil 6 minutes or until blackened. Place in a zip-top plastic bag; seal. Let stand 15 minutes. Peel and discard skins, stems, and seeds. Cut chiles into thin strips.
Combine lime juice and next 5 ingredients (through cumin) in a large bowl, stirring with a whisk. Add chile strips and salad greens; toss gently to coat.