There are countless versions of the traditional Mexican mole sauce, most with dozens of ingredients. We've adapted this version for practicality and availability for an easy weeknight meal.
In a 4- to 5-qt. pot stir together the first ten ingredients (through cinnamon). Bring to boiling, stirring constantly (mixture will be thick).
Reduce heat and add chicken to tomato mixture. Sprinkle with salt and pepper. Simmer, covered, 1 hour or until chicken is tender, turning chicken once. Remove chicken. Using two forks, shred chicken; discard bones. Return chicken to pot.
Spoon chicken mixture on tostada shells. Top with cheese, green onions, and cilantro.
To soak peppers, place in a small heat-proof bowl. Add 1/2 cup boiling water; let stand 20 minutes. Drain.