This delicious Chili has a great flavor from the chili's but not too hot.
Liberally sprinkle salt and pepper on chicken. Heat the oil in Dutch oven over medium high heat until just smoking. Add chicken skin side down and cook without moving until skin is golden brown (4 minutes). Using tongs, turn chicken- lightly brown the other side (2 minutes). Transfer chicken to plate; remove and discard skin.
Remove ribs and seeds from the jalapenos. Mince the flesh. Food process half the poblano, anaheim, and leeks until consistency of chunky salsa. (10-12 1 second pulses) Transfer to a bowl. Repeat with remaining poblano, anaheim and leeks. Combine with first batch. (Don't clean food processor)
Pour off all but 1 tbsp fat from dutch oven (add vegi oil if needed) and reduce heat to medium. Add jalapenos, chili-onion mixture, garlic, cumin, coriander, and 1/4 tsp of salt. Cover and cook, stirring occationally, untili vegies soften (10 minutes). Remove pot from heat
Transfer 1 c cooked vegitable mixture to food processor. Add 1 c beans and 1 c broth. Process until smooth (20 seconds). Add vegetable- bean mixture, remaining 2 c broth, chicken breasts to Dutch oven. Bring to boil over medium-high heat. Reduce heat to medium-low and simmer, covered, stirring occasionally, until chicken registers 160 degrees (15-20 minutes)
Using tongs, transfer chickenn to large plate. Stir in remaining beans and continue to simmer, uncovered, utnil beans are heated through and chili has slightly thickened (10 minutes)
Mince remaining jalapeno (remove ribs and seeds) and set aside. Shred chicken into bite-sized pieces. Stir shredded chicken, lime jice, cilantro, and remaining minced jalapeno into chili and return to simmer. Adjust seasonings with salt and pepper and serve.