Some people dislike cilantro's pungent scent and find it soapy-tasting, but others are passionate about the bold, tangy flavor, which is sagelike with citrus overtones. The leaf is best when used fresh. The whole or ground seeds, which have a more citrusy taste, are used in baked goods and beverages and with sausages, vegetables, and curries.
Fiery habanero chilies will make this dish sizzle; for a milder taste, choose poblano or Anaheim chilies.
Place chicken breasts between sheets of plastic wrap; flatten with a mallet or rolling pin. Place chicken in a resealable plastic bag. Combine minced cilantro, oil, lime juice, garlic, and seasonings in a jar; shake well and pour over chicken. Seal and marinate in the refrigerator for 1 hour.
Meanwhile husk the tomatillos. Grill the tomatillos, tomatoes, and chilies until their skins are blackened. Peel and core the tomatoes and cut into chunks. Remove peels from the chilies. Add grilled vegetables to a food processor bowl, along with the onion and cilantro leaves. Process until vegetables are uniformly chopped but still chunky. Stir in lime juice and add salt to taste.
Grill marinated chicken until cooked through, about 5 minutes per side. To serve, heap salsa over chicken breasts and garnish with cilantro sprigs.