In a 4- to 5-quart pan over high heat, bring turkey breast, broth, and onion to a boil. Cover, reduce heat, and simmer until turkey is no longer pink in center of thickest part (cut to test), 8 to 10 minutes.
With a slotted spoon, lift turkey from broth. When cool enough to touch, in 5 to 6 minutes, tear meat into fine shreds.
Meanwhile, wearing gloves, cut out and discard chili seeds and veins. Finely chop chilies.
Whisk masa into broth. Add tomatoes (with juice), then chilies to taste. Bring to a boil over high heat, stirring often. Reduce heat and simmer to blend flavors, about 5 minutes. Add turkey and stir just until hot, 1 to 2 minutes.
Ladle into wide bowls. Garnish with cilantro sprigs.